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SPIRES-BOOKS: FIND KEYWORD PROJECTIVE GEOMETRY *END*INIT* use /tmp/qspiwww.webspi1/5387.25 QRY 131.225.70.96 . find keyword projective geometry ( in books using www Cover
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Call number:9783319393391:ONLINE Show nearby items on shelf
Title:Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014
Author(s):
Date:2017
Size:1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.)
Contents:Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic
vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular
varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded
topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces
ISBN:9783319393391
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds
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Call number:0471113158:ONLINE Show nearby items on shelf
Title:Affine and Projective Geometry
Author(s): Bennett
Date:1995
Publisher:Wiley-Interscience
Size:1 online resource (249 p.)
ISBN:9780471113157
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:SPRINGER-2016-9789462391925:ONLINE Show nearby items on shelf
Title:Cartan Geometries and their Symmetries A Lie Algebroid Approach
Author(s): Mike Crampin
Date:2016
Size:1 online resource (290 p.)
Note:10.2991/978-94-6239-192-5
Contents:Lie groupoids and Lie algebroids -- Connections on Lie groupoids and Lie algebroids -- Groupoids of fibre morphisms -- Four case studies -- Symmetries -- Cartan geometries -- A comparison with alternative approaches -- Infinitesimal Cartan geomet ries on TM -- Projective geometry: the full version -- Conformal geometry: the full version -- Developments and geodesics -- Cartan theory of second-order differential equations.
ISBN:9789462391925
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Atlantis Studies in Variational Geometry: 4
Keywords: Mathematics , Differential geometry , Mathematics , Differential Geometry
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Call number:SPRINGER-2016-9783662454503:ONLINE Show nearby items on shelf
Title:The Universe of Conics From the ancient Greeks to 21st century developments
Author(s): Georg Glaeser
Date:2016
Edition:1st ed. 2016
Size:1 online resource (488 p.)
Note:10.1007/978-3-662-45450-3
Contents:1 Introduction -- 2 Euclidean plane -- 3 Differential Geometry -- 4 Eucledian 3-space -- 5 Projective Geometry -- 6 Projective conics -- 7 Polarities and pencils -- 8 Affine Geometry -- 9 Special problems -- 10 Other geometries -- Index
ISBN:9783662454503
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Applied mathematics , Engineering mathematics , Geometry , Mathematics , Geometry , Applications of Mathematics
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Call number:SPRINGER-2016-9783319323152:ONLINE Show nearby items on shelf
Title:Hyperbolicity of Projective Hypersurfaces
Author(s): Simone Diverio
Date:2016
Size:1 online resource (89 p.)
Note:10.1007/978-3-319-32315-2
Contents:- Introduction -- Kobayashi hyperbolicity: basic theory -- Algebraic hyperbolicity -- Jets spaces -- Hyperbolicity and negativity of the curvature -- Hyperbolicity of generic surfaces in projective 3-space -- Algebraic degeneracy for projective hyp ersurfaces
ISBN:9783319323152
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:IMPA Monographs : 5
Keywords: Mathematics , Algebraic geometry , Functions of complex variables , Differential geometry , Mathematics , Differential Geometry , Algebraic Geometry , Several Complex Variables and Analytic Spaces
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Call number:SPRINGER-2016-9783319299594:ONLINE Show nearby items on shelf
Title:K3 Surfaces and Their Moduli
Author(s):
Date:2016
Size:1 online resource (3 p.)
Note:10.1007/978-3-319-29959-4
Contents:Introduction -- Samuel Boissière, Andrea Cattaneo, Marc Nieper-Wisskirchen, and Alessandra Sarti: The automorphism group of the Hilbert scheme of two points on a generic projective K3 surface -- Igor Dolgachev: Orbital counting of curves on algebra ic surfaces and sphere packings -- V. Gritsenko and K. Hulek: Moduli of polarized Enriques surfaces -- Brendan Hassett and Yuri Tschinkel: Extremal rays and automorphisms of holomorphic symplectic varieties -- Gert Heckman and Sander Rieken: An odd presen tation for W(E_6) -- S. Katz, A. Klemm, and R. Pandharipande, with an appendix by R. P. Thomas: On the motivic stable pairs invariants of K3 surfaces -- Shigeyuki Kondö: The Igusa quartic and Borcherds products -- Christian Liedtke: Lectures on supersing ular K3 surfaces and the crystalline Torelli theorem -- Daisuke Matsushita: On deformations of Lagrangian fibrations -- G. Oberdieck and R. Pandharipande: Curve counting on K3 x E, the Igusa cusp form X_10, and descendent integration -- Keiji
Oguiso: Simple abelian varieties and primitive automorphisms of null entropy of surfaces -- Ichiro Shimada: The automorphism groups of certain singular K3 surfaces and an Enriques surface -- Alessandro Verra: Geometry of genus 8 Nikulin surfaces and rationality of their moduli -- Claire Voisin: Remarks and questions on coisotropic subvarieties and 0-cycles of hyper-Kähler varieties
ISBN:9783319299594
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 315
Keywords: Mathematics , Algebraic geometry , Mathematics , Algebraic Geometry
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Call number:SPRINGER-2016-9783319267654:ONLINE Show nearby items on shelf
Title:On the Geometry of Some Special Projective Varieties
Author(s): Francesco Russo
Date:2016
Edition:1st ed. 2016
Size:1 online resource (232 p.)
Note:10.1007/978-3-319-26765-4
Contents:Preface.-Introduction -- 1.Tangent cones, tangent spaces, tangent stars secant, tangent and tangent star varieties to an algebraic variety -- 2.Basics of Deformation Theory of Rational Curves on Projective Varieties -- 3.Fulton-Hansen Connectedness Theorem, Scorza Lemma and their applications to projective geometry -- 4.Local quadratic entry locus manifolds and conic connected manifolds -- 5.Hartshorne Conjectures and Severi varieties -- 6.Varieties n-covered by curves of a fixed degree and the XJC -- 7. Hypersurfaces with vanishing hessian.-Bibliography
ISBN:9783319267654
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes of the Unione Matematica Italiana: 18
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Geometry , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Geometry
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Call number:SPRINGER-2016-9781447167907:ONLINE Show nearby items on shelf
Title:General Galois Geometries
Author(s): J.W.P Hirschfeld
Date:2016
Edition:1st ed. 2016
Size:1 online resource (409 p.)
Note:10.1007/978-1-4471-6790-7
Contents:Preface -- Terminology -- Quadrics -- Hermitian varieties -- Grassmann varieties -- Veronese and Serge varieties -- Embedded geometries -- Arcs and Caps -- Ovoids, spreads and m-systems of finite polar spaces -- References -- Index
ISBN:9781447167907
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Projective geometry , Combinatorics , Mathematics , Projective Geometry , Combinatorics , Algebraic Geometry
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Call number:SPRINGER-2014-9784431545712:ONLINE Show nearby items on shelf
Title:Nevanlinna Theory in Several Complex Variables and Diophantine Approximation [electronic resource]
Author(s): Junjiro Noguchi
Jrg Winkelmann
Date:2014
Publisher:Tokyo : Springer Japan : Imprint: Springer
Size:1 online resource
Note:The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with ninechapters systematically de scribes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 tothe current state of research. Chapter 2 present s the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension isdescribed. In Chap. 3 the Second Main Theorem for differentiably non-d egenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem forentire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Ca rtan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraicvarieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of N oguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to thenotion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are dis cussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt withfrom the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is d iscussed. Finally, in Chap. 9, the theorems of Roth, Schmidt,Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4,
Contents:Nevanlinna Theory of Meromorphic Functions
First Main Theorem
Differentiably Non
Degenerate Meromorphic Maps
Entire Curves into Algebraic Varieties
Semi
Abelian Varieties
Entire Curves into Semi
Abelian Varieties
Kobayashi Hyperbolicity
Nevanlinna Theory over Function Fields
Diophantine Approximation
Bibliography
Index
Symbols
ISBN:9784431545712
Series:eBooks
Series:SpringerLink
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v350
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Differential equations, partial , Number theory
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Call number:SPRINGER-2014-9783319056814:ONLINE Show nearby items on shelf
Title:Automorphisms in Birational and Affine Geometry [electronic resource] : Levico Terme, Italy, October 2012
Author(s): Ivan Cheltsov
Ciro Ciliberto
Hubert Flenner
James McKernan
Yuri G Prokhorov
Mikhail Zaidenberg
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinitedimensional. The collect ion covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraicgroup actions and automorphism groups. It pres ents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraicgeometry and affine and complex algebraic geometry, including Mori theo ry and algebraic group actions, this book is the result of ensuing talks and discussions from the conference Groups of Automorphisms in Birational and AffineGeometry held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highl ighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacentfields
Contents:Preface
Part I Birational automorphisms
H. Ahmadinezhad: Singular del Pezzo fibrations and birational rigidity
I. Arzhantsev, A. Popovskiy: Additive actions on projective hypersurfaces
J. Blanc, F. Mangolte: Cremona groups of real surfaces
M. Brion: On automorphisms and endomorphisms of projective varieties
I. Cheltsov: Del Pezzo surfaces and local inequalities
T. de Fernex: Fano hypersurfaces and their birational geometry
T. Eckl, A. Pukhlikov: On the locus of non
rigid hypersurfaces
S. Lamy: On the genus of birational maps between 3
folds
A. Massarenti, M. Mel
ISBN:9783319056814
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v79
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic
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Call number:SPRINGER-2014-9783319052540:ONLINE Show nearby items on shelf
Title:Trends in Contemporary Mathematics [electronic resource]
Author(s): Vincenzo Ancona
Elisabetta Strickland
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book covers a wide spectrum of hot topics and current trends in mathematics, including noncommutative algebra via deformation theory, optimal transportation, nonlinear potential theory,kinetic theory and gas dynamics,geometric numerical integrat ion, finite simple groups of small essential dimension, optimal control problems, extended Dynkin diagrams, spin glasses, aspherical closed manifolds, Boltzmann systems, birational geometry of projectivevarieties and directed graphs, nonlinear diffusion, geometric constructions of extremal metrics on complex manifolds, and Pells equation in polynomials. The book comprises a selection of contributions by leading internationalmathematicians who were speakers at the INdAM Day, an initiative dating back to 20 04 at which the most recent developments in contemporary mathematics are presented
Contents:1 F. Guerra: Interpolation and comparison methods in the mean field spin glass model
2 A. De Sole, V.G. Kac, D. Valeri: Integrability of dirac reduced Bi
Hamiltonian equations
3 W. Luck: Some open problems about aspherical closed manifolds abstract
4 P. Etingof: Exploring noncommutative algebras via deformation theory
5 G. Lancia: Mathematical models and solutions for the analysis of human genotypes
6 M. Manetti: Kodaira
Spencer formality of products of complex manifolds
7 O. Debarre, B. Lass: Monomial transformations of the projective space
8 J.L. Vazquez: Progress in the
ISBN:9783319052540
Series:eBooks
Series:SpringerLink
Series:Springer INdAM Series, 2281-518X : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Global analysis (Mathematics) , Differential equations, partial , Computer science Mathematics
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Call number:SPRINGER-2014-9783319048703:ONLINE Show nearby items on shelf
Title:Combinatorial Algebraic Geometry [electronic resource] : Levico Terme, Italy 2013, Editors: Sandra Di Rocco, Bernd Sturmfels
Author(s): Aldo Conca
Sandra Di Rocco
Jan Draisma
June Huh
Bernd Sturmfels
Filippo Viviani
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry. The aim of this volume is tointroduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varietiesendowed with a rich combinatorial structure. Rele vant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications
Contents:Koszul algebras, Koszul homology and syzygies
Infinite
dimensional systems of polynomial equations with symmetry
Maximum Likelihood Geometry
Linear Toric fibrations and Cayley polytopes
Toroidal compactifications and tropicalizations of moduli spaces
ISBN:9783319048703
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2108
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Combinatorics
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Call number:SPRINGER-2014-9783319017334:ONLINE Show nearby items on shelf
Title:An Algebraic Approach to Geometry [electronic resource] : Geometric Trilogy II
Author(s): Francis Borceux
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level andalgebraic geometry at a gradua te level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates andequations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes, ) and second degree (ellipses, hyperboloids, ) geometricfigures, in the affine, the Euclidean, the Hermitian and the projective contexts. Bu t recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, likein spaces constructed on finite fields. And of course, why not also turn our attention to geometric figur es of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes usefulalgebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer p aradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all thosewho have to teach or study linear geometry: affine, Euclidean, Hermitian, projective it is also of great interest to those who do not want to restrict t hemselves to the undergraduate level of geometric figures of degree one or two
Contents:Introduction
Preface
1.The Birth of Analytic Geometry
2.Affine Geometry
3.More on Real Affine Spaces
4.Euclidean Geometry
5.Hermitian Spaces
6.Projective Geometry
7.Algebraic Curves
Appendices:A. Polynomials Over a Field
B. Polynomials in Several Variables
C. Homogeneous Polynomials
D. Resultants
E. Symmetric Polynomials
F. Complex Numbers
G. Quadratic Forms
H. Dual Spaces
Index
Bibliography
ISBN:9783319017334
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry
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Call number:SPRINGER-2014-9783319017303:ONLINE Show nearby items on shelf
Title:An Axiomatic Approach to Geometry [electronic resource] : Geometric Trilogy I
Author(s): Francis Borceux
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomaticgeometry: Euclidean, non-Euc lidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions ofwhich have led to various presently very active dom ains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all,several parallels) has led to the emergence of mathematical theories based o n an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomaticgeometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection ofthe angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundred s of figures that support intuition. Through 35 centuries of the history of geometry, discover the birthand follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the vario us levels of rigor which successively established themselves through the centuries.Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world ofaxiomatic mathematical theories!
Contents:Introduction
Preface
1.The Prehellenic Antiquity
2.Some Pioneers of Greek Geometry
3.Euclids Elements
4.Some Masters of Greek Geometry
5.Post
Hellenic Euclidean Geometry
6.Projective Geometry
7.Non
Euclidean Geometry
8.Hilberts Axiomatics of the Plane
Appendices: A. Constructibily
B. The Three Classical Problems
C. Regular Polygons
Index
Bibliography
ISBN:9783319017303
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry
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Call number:SPRINGER-2013-9783642362439:ONLINE Show nearby items on shelf
Title:Real Algebraic Geometry [electronic resource]
Author(s): Vladimir I Arnold
Ilia Itenberg
Viatcheslav Kharlamov
Eugenii I Shustin
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900),Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance ofthis problem (including its numerous applications ), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered)
Note:Springer eBooks
Contents:Publisher's Foreword
Editors' Foreword
Introduction
2 Geometry of Conic Sections
3 The Physics of Conic Sections and Ellipsoids
4 Projective Geometry
5 Complex Algebraic Curves
6 A Problem for School Pupils
A Into How Many Parts do n Lines Divide the Plane?
Editors' Comments on Gudkov's Conjecture
Notes
ISBN:9783642362439
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714 : v66
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Geometry , Mathematical physics
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Call number:SPRINGER-2013-9783642344534:ONLINE Show nearby items on shelf
Title:Diagram Geometry [electronic resource] : Related to Classical Groups and Buildings
Author(s): Francis Buekenhout
Arjeh M Cohen
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective.Projective and affine geome try are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differsfrom Tits' comprehensive treatment in that it use s Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light onmatroid theory is shed from the point of view of geometry with linear diagra ms. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from thediagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so grad uate students will be able to follow the arguments without needing recourse to further literature. A strong point of the bookis the density of examples.
Note:Springer eBooks
Contents:1. Geometries
2. Diagrams
3. Chamber Systems
4. Thin Geometries
5. Linear Geometries
6. Projective and Affine Spaces
7. Polar Spaces
8. Projective Embeddings of Polar Spaces
9. Embedding Polar Spaces in Absolutes
10. Classical Polar Spaces
11. Buildings
Bibliography
Index
ISBN:9783642344534
Series:e-books
Series:SpringerLink (Online service)
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v57
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry
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Call number:SPRINGER-2013-9783642317941:ONLINE Show nearby items on shelf
Title:Foundations of Geometric Algebra Computing [electronic resource]
Author(s): Dietmar Hildenbrand
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The author defines Geometric Algebra Computing as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay thefoundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometricalgebra as a 5D extension of the 4D projective geometric alg ebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometricalgebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations in Part II he explains the interactive handling ofgeometric algebra and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book iswritten in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computationalengineering, and mathematics
Note:Springer eBooks
Contents:Chap. 1 Introduction
Chap. 2 Mathematical Introduction
Chap. 3 The Conformal Geometric Algebra
Chap. 4 Maple and the Identification of Quaternions and Other Algebras
Chap. 5 Fitting of Planes or Spheres into Point Sets
Chap. 6 Geometric Algebra Tutorial Using CLUCalc
Chap. 7 Inverse Kinematics of a Simple Robot
Chap. 8 Robot Grasping an Object
Chap. 9 Efficient Computer Animation Application in CGA
Chap. 10 Using Gaalop for Performant Geometric Algebra Computing
Chap. 11 Collision Detection Using the Gaalop Precompiler
Chap. 12 Gaalop Precompiler for GPGPUs
ISBN:9783642317941
Series:e-books
Series:SpringerLink (Online service)
Series:Geometry and Computing, 1866-6795 : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Computer science , Computer vision , Geometry , Engineering mathematics
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Call number:SPRINGER-2013-9783642309946:ONLINE Show nearby items on shelf
Title:Linear Algebra and Geometry [electronic resource]
Author(s): Igor R Shafarevich
Alexey O Remizov
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements ofmatrix theory and continue s with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but areusually not covered in such courses: exterior alge bras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitelygenerated periodic modules (similar to Jordan normal forms of linear opera tors). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equationsand differential geometry, as well as from mechanics and physics
Note:Springer eBooks
Contents:Preface
Preliminaries
1. Linear Equations
2. Matrices and Determinants
3. Vector Spaces
4. Linear Transformations of a Vector Space to Itself
5. Jordan Normal Form
6. Quadratic and Bilinear Forms
7. Euclidean Spaces
8. Affine Spaces
9. Projective Spaces
10. The Exterior Product and Exterior Algebras
11. Quadrics
12. Hyperbolic Geometry
13. Groups, Rings, and Modules
14. Elements of Representation Theory
Historical Note
References
Index
ISBN:9783642309946
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Geometry
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Call number:SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf
Title:Complex Kleinian Groups [electronic resource]
Author(s): Angel Cano
Juan Pablo Navarrete
Jos Seade
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds
Note:Springer eBooks
Contents:Preface
Introduction
Acknowledgments
1 A glance of the classical theory
2 Complex hyperbolic geometry
3 Complex Kleinian groups
4 Geometry and dynamics of automorphisms of P2C
5 Kleinian groups with a control group
6 The limit set in dimension two
7 On the dynamics of discrete subgroups of PU(n,1)
8 Projective orbifolds and dynamics in dimension two
9 Complex Schottky groups
10 Kleinian groups and twistor theory
Bibliography
Index.
ISBN:9783034804813
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v303
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial
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Call number:SPRINGER-2013-9781461464822:ONLINE Show nearby items on shelf
Title:Birational Geometry, Rational Curves, and Arithmetic [electronic resource]
Author(s): Fedor Bogomolov
Brendan Hassett
Yuri Tschinkel
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis onapplications to arithmeti c questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the studyof rational and integral points on algebraic var ieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on thevariety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of referencefor experts working on related problems. Topics that will be addressed include: birational pro perties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, conesof rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framewo rk of the Minimal Model Program
Note:Springer eBooks
Contents:Foreword
Introduction
A. Bertram and I. Coskun, The birational geometry of the Hilbert scheme of points on surfaces
F. Bogomolov and Ch. Bhning, Isoclinism and stable cohomology of wreath products
F. Bogomolov, I. Karzhemanov, and K. Kuyumzhiyan, Unirationality and existence of infinitely transitive models
I. Cheltsov, L. Katzarkov, and V. Przyjalkowski, Birational geometry via moduli spaces
O. Debarre, Curves of low degrees on projective varieties
S. Kebekus, Uniruledness criteria and applications
S. Kovcs, The cone of curves of K3 surfaces revisited
V. Lazi,
ISBN:9781461464822
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Geometry , Number theory
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Call number:SPRINGER-2013-9781461459873:ONLINE Show nearby items on shelf
Title:Introduction to Commutative Algebra and Algebraic Geometry [electronic resource]
Author(s): Ernst Kunz
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Originally published in 1985, this classic textbook is an English translation of Einfhrung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhuser Classics series, the publisher is proud to makeIntroduction to Commutati ve Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representationof algebraic varieties as intersections of the least possible number of hypersurfaces anda closely related problemwith the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basicconcepts of commutative algebra and algebraic geometry and proves many facts whic h can then serve as a basic stock for a deeper study of these subjects
Note:Springer eBooks
Contents:Foreword
Preface
Preface to the English Edition
Terminology
Algebraic varieties
Dimension
Regular and rational functions on algebraic varieties
The local
global principle in commutative algebra
On the number of equations needed to describe an algebraic variety
Regular and singular points of algebraic varieties
Projective Resolutions
Bibliography
List of Symbols
Index.
ISBN:9781461459873
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic
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Call number:SPRINGER-2013-9781447148296:ONLINE Show nearby items on shelf
Title:Algebraic Geometry and Commutative Algebra [electronic resource]
Author(s): Siegfried Bosch
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover,Grothendiecks schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved theway to spectacular progress such as the proof of Fermats Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broadentheir view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter ofthe book is preceded by a motivating introduction with an informal discussion of the contents. Typical exa mples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourselfor for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature
Note:Springer eBooks
Contents:Rings and Modules
The Theory of Noetherian Rings
Integral Extensions
Extension of Coefficients and Descent
Homological Methods: Ext and Tor
Affine Schemes and Basic Constructions
Techniques of Global Schemes
Etale and Smooth Morphisms
Projective Schemes and Proper Morphisms
ISBN:9781447148296
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra
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Call number:SPRINGER-2013-9781447146315:ONLINE Show nearby items on shelf
Title:Symmetry and Pattern in Projective Geometry [electronic resource]
Author(s): Eric Lord
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods.The analytic approach is based on homogeneous coordinates. Briefintroductions to Plcker coord inates and Grassmann coordinates are also presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensionsand consequences of basic theorems such as those of P appus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of H S M Coxeter,who is considered one of the great geometers of the twentieth century, are al so discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurationsdiscovered by Coxeter. This book will be appreciated by mathematics undergraduate students and thos e wishing to learn more about the subject of geometry. Subject and theorems that are often considered quite complicated are madeaccessible and presented in an easy-to-read and enjoyable manner.
Note:Springer eBooks
Contents:Foundations: the Synthetic Approach
The Analytic Approach
Linear Figures
Quadratic Figures
Cubic Figures
Quartic Figures
Finite Geometries
ISBN:9781447146315
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra Data processing
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Call number:SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf
Title:New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number
Author(s): Garret Sobczyk
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s
Note:Springer eBooks
Contents:1 Modular Number Systems
2 Complex and Hyperbolic Numbers
3 Geometric Algebra
4 Vector Spaces and Matrices
5 Outer Product and Determinants
6 Systems of Linear Equations
7 Linear Transformations on R^n
8 Structure of a Linear Operator
9 Linear and Bilinear Forms
10 Hermitian Inner Product Spaces
11 Geometry of Moving Planes
12 Representations of the Symmetric Group
13 Calculus on m
Surfaces
14 Differential Geometry of Curves
15 Differential Geometry of k
Surfaces
16 Mappings Between Surfaces
17 Non
Euclidean and Projective Geometries
18 Lie Gr
ISBN:9780817683856
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2012-9783642309649:ONLINE Show nearby items on shelf
Title:Gems of Geometry [electronic resource]
Author(s): John Barnes
Date:2012
Edition:2nd ed. 2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Based on a series of lectures for adult students at Reading and Oxford University in the UK, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination.The author's infectio us enthusiasm is put to use in explaining a range of topics, starting with the Golden Number and taking the reader on a geometrical journey covering topics such as Shapes and Solids, the Fourth Dimension,Projective Geometry and Topology, Chaos and Fractal s, Steiner's porism, Soddy's Hexlet, Einstein's Theories of Relativity and finishing up with the amazing world of Crystals. Aimed at a general readership, and requiring only a basicunderstanding of mathematics, the text includes a wealth of the author's own diagrams and illustrations, of which many are in stereo. Equally ideal as an educational gift for a youngster or as a nostalgic journey back into the worldof mathematics for older readers, John Barnes' book brings enlightenment and entertainment. u nlike your average student textbook, this is a book designed to be dipped into, explored, enjoyed and savoured. PLUS.MATHS.ORGGems of Geometry is a delightful little book it is exactly the kind of thing that I would have loved to have had as a child Roger Penrose
Note:Springer eBooks
Contents:1 The Golden Number
2 Shapes and Solids
3 The Forth Dimension
4 Projective Geometry
5 Topology
6 Bubbles
7 Harmony of the Spheres
8 Chaos and Fractals
9 Relativity
10 Finale
A More on Four
B Crystals
C Stability
D Stereo Images
E Schlegel Images
F Stability
G Fanoland
Bibliography
Index
ISBN:9783642309649
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry
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Call number:SPRINGER-2012-9783642291630:ONLINE Show nearby items on shelf
Title:Geometry by Its History [electronic resource]
Author(s): Alexander Ostermann
Gerhard Wanner
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications,while more recent fi ndings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry,vector algebra and matrices are treated in chapters 9 and 10. The last chapteroffers an introduction to projective geometry, which emerged in the19th century. Complemented by numerous examples, exercises, figures and pictures, thebook offers both motivation and insightful explanations, and provid es stimulating and enjoyable reading for students and teachers alike
Note:Springer eBooks
Contents:Preface
Part I: Classical Geometry
Thales and Pythagoras
The Elements of Euclid
Conic Sections
Further Results on Euclidean Geometry
Trigonometry
Part II: Analytic Geometry
Descartes' Geometry
Cartesian Coordinates
To be Constructible, or not to be
Spatial Geometry and Vector Algebra
Matrices and Linear Mappings
Projective Geometry
Solutions to Exercises
References
Figure Source and Copyright
Index
ISBN:9783642291630
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Geometry
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Call number:SPRINGER-2012-9783642248887:ONLINE Show nearby items on shelf
Title:Finsler Geometry [electronic resource] : An Approach via Randers Spaces
Author(s): Xinyue Cheng
Zhongmin Shen
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Finsler Geometry: An Approach via Randers Spaces exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from theresearch on General Relati vity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essentialfindings on Randers metrics but also the core i deas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry orrelated natural fields. Xinyue Cheng is a Professor at the School of Ma thematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana UniversityPurdue University, USA
Note:Springer eBooks
Contents:Randers Spaces
Randers Metrics and Geodesics
Randers Metrics of Isotropic S
Curvature
Riemann Curvature and Ricci Curvature
Projective Geometry of Randers Spaces
Randers Metrics with Special Riemann Curvature Properties
Randers Metrics of Weakly Isotropic Flag Curvature
Projectively Flat Randers Metrics
Conformal Geometry of Randers Metrics
Dually Flat Randers Metrics
ISBN:9783642248887
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2012-9783642244155:ONLINE Show nearby items on shelf
Title:The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type [electronic resource]
Author(s): Thomas H Otway
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometricvariational theory, and the th eory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems that can be formulated for Keldysh-type equations,one of the two main classes of linear elliptic-hyperb olic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entireboundary) are both considered. Emphasis is placed on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space, and specific applications to plasma physics, optics, and analysison projective spaces are discussed
Note:Springer eBooks
Contents:1 Introduction
2 Mathematical Preliminaries
3 The Equation of Cinquini
Cibrario
4 The Cold Plasma Model
5 Light near a Caustic
6 Projective Geometry
ISBN:9783642244155
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2043
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial
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Call number:SPRINGER-2012-9783642192258:ONLINE Show nearby items on shelf
Title:A Royal Road to Algebraic Geometry [electronic resource]
Author(s): Audun Holme
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to readall of his work Eleme nts. Euclid is said to have answered: There is no royal road to geometry! The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royalroad to algebraic geometry. From a point of depart ure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendiecks theory of schemes. Contemporary homological tools areexplained. The reader will follow a directed path leading up to the main elem ents of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to awonderful field of research. The greatest scientific experience of a lifetime!
Note:Springer eBooks
Contents:Part I Curves: 1 Affine and Projective Space
2 Curves in A2 k and in P2
3 Higher Geometry in the Projective Plane
4 Plane Curves and Algebra
5 Projective Varieties in PNk
Part II Introduction to Grothendiecks Theory of Schemes: 6 Categories and Functors
7 Constructions and Representable Functors
8 Abelian Categories
9 The Concept of Spec(A)
10 The Category of Schemes
11 Properties of Morphisms of Schemes
12 Modules, Algebras and Bundles on a Scheme
13 More Properties of Morphisms, Scheme Theoretic Image and the Sorite
14 Projective Schemes and Bu
ISBN:9783642192258
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Geometry , Algebraic topology
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Call number:SPRINGER-2012-9783034804936:ONLINE Show nearby items on shelf
Title:Plane Algebraic Curves [electronic resource] : Translated by John Stillwell
Author(s): Egbert Brieskorn
Horst Knrrer
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source ofinspiration and topic of resear ch to this day. Arising from notes for a course given at the University of Bonn in Germany, Plane Algebraic Curves reflects the authors concern for the student audience through emphasis uponmotivation, development of imagination, and understanding of basi c ideas. As classical objects, curves may be viewed from many angles this text provides a foundation for the comprehension and exploration of modern work onsingularities. --- In the first chapter one finds many special curves with very attractive geometr ic presentations the wealth of illustrations is a distinctive characteristic of this book and an introduction toprojective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezouts theorem and a detailed discuss ion of cubics. The heart of this book and how else could it be with the first author is the chapter on the resolution of singularities (always over the complex numbers). () Especially remarkable is the outlook to further work on the topics discussed, wit h numerous references to the literature. Many examplesround off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)
Note:Springer eBooks
Contents:I. History of algebraic curves
1. Origin and generation of curves
2. Synthetic and analytic geometry
3. The development of projective geometry
II. Investigation of curves by elementary algebraic methods
4. Polynomials
5. Definition and elementary properties of plane algebraic curves
6. The intersection of plane curves
7. Some simple types of curves
III. Investigation of curves by resolution of singularities
8. Local investigations
9. Global investigations
Bibliography
Index
ISBN:9783034804936
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Algebraic topology
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Call number:SPRINGER-2012-9783034804202:ONLINE Show nearby items on shelf
Title:Classical Geometries in Modern Contexts [electronic resource] : Geometry of Real Inner Product Spaces Third Edition
Author(s): Walter Benz
Date:2012
Edition:3rd ed. 2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolicgeometry with respect to nat ural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Mbius and Lie as well as geometries where Lorentz transformations play thekey role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentztransformations. A real benefit is the dimension-free approach to important geome trical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these samespaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz -Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result inthis edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the ge ometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all xin X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for read ing this book are basic linear algebra and basic 2- and 3-dimensional real geometry.This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in m odern and general contexts
Note:Springer eBooks
Contents:Preface
1 Translation Groups
2 Euclidean and Hyperbolic Geometry
3 Sphere Geometries of Mbius and Lie
4 Lorentz Transformations
5 Projective Mappings, Isomorphism Theorems
6 Planes of Leibniz, Lines of Weierstrass, Varia
A Notation and symbols
B Bibliography
Index
ISBN:9783034804202
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Mathematical physics
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Call number:SPRINGER-2011-9783834881595:ONLINE Show nearby items on shelf
Title:Lectures on Algebraic Geometry II [electronic resource] : Basic Concepts, Coherent Cohomology, Curves and their Jacobians
Author(s): Gnter Harder
Date:2011
Publisher:Wiesbaden : Vieweg+Teubner
Size:1 online resource
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Note:In this second volume of Lectures on Algebraic Geometry, the author starts with some foundational concepts in the theory of schemes and gives a somewhat casual introduction into commutative algebra. After that he proves thefiniteness results for cohe rent cohomology and discusses important applications of these finiteness results. In the two last chapters, curves and their Jacobians are treated and some outlook into further directions of research isgiven. The first volume is not necessarily a prerequi site for the second volume if the reader accepts the concepts on sheaf cohomology. On the other hand, the concepts and results in the second volume have been historically inspired bythe theory of Riemann surfaces. There is a deep connection between these two volumes, in spirit they form a unity. Basic concepts of the Theory of Schemes - Some Commutative Algebra - Projective Schemes - Curves and the Theorem ofRiemann-Roch - The Picard functor for curves and Jacobians. Prof. Dr. Gnter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany
Note:Springer eBooks
ISBN:9783834881595
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry
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Call number:SPRINGER-2011-9783642209727:ONLINE Show nearby items on shelf
Title:Foundations of Incidence Geometry [electronic resource] : Projective and Polar Spaces
Author(s): Johannes Ueberberg
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Incidence geometry is a central part of modern mathematicsthat has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polarspaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets arepresented in this volume. Incidence geometry is devel oped along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. Morethan 200 figures make even complicated proofs accessible to the reader
Note:Springer eBooks
Contents:I Projective and Affine Geometries
1. Introduction
2. Geometries and Pregeometries
3. Projective and Affine Planes
4. Projective Spaces
5. Affine Spaces
6. A Characterization of Affine Spaces
7. Residues and Diagrams
8. Finite geometries
II Isomorphisms and Collineations
1. Introduction
2. Morphisms
3. Projections
4. Collineations of projective and affine spaces
5. Central Collineations
6. The Theorem of Desargues
III Projective Geometry over a Vector Space
1. Introduction
2. The Projective Space P(V)
3. Homogeneous Coordinates of Projec
ISBN:9783642209727
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry
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Call number:SPRINGER-2011-9783642203008:ONLINE Show nearby items on shelf
Title:Complex and Differential Geometry [electronic resource] : Conference held at Leibniz Universitt Hannover, September 14 18, 2009
Author(s): Wolfgang Ebeling
Klaus Hulek
Knut Smoczyk
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This volume contains the Proceedings of the conference Complex and Differential Geometry 2009, held at Leibniz Universitt Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists fromdifferential geometry and (complex ) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in(classical) algebraic geometry through complex geometr y, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology
Note:Springer eBooks
Contents:Participants
Surfaces of general type with geometric genus zero: a survey
Holomorphic symplectic geometry: a problem list
Generalized Lagrangian mean curvature flow in Khler manifolds that are almost Einstein
Einstein metrics and preserved curvature conditions for the Ricci flow
Differential Harnack Estimates for Parabolic Equations
Euler characteristic of a complete intersection
Cremona special sets of points in products of projective spaces
Stable bundles and polyvector fields
Buser
Sarnak invariant and projective normality of abelian varieties
Complete Kahl
ISBN:9783642203008
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics, 2190-5614 : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2011-9783642183997:ONLINE Show nearby items on shelf
Title:Homogeneous Spaces and Equivariant Embeddings [electronic resource]
Author(s): D.A Timashev
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standardreasons of algebraic geomet ry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally,open embeddings of a given homogeneous space. S uch equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of combinatorial nature (the Luna-Vusttheory) and description of various geometric and representation-theoretic prop erties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest inthe scope of this book. Spherical varieties include many classical examples, such as Grassmannians , flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the importantissues, including the recent substantial progress obtained in and around the theory of spherical varieties
Note:Springer eBooks
Contents:Introduction
1 Algebraic Homogeneous Spaces
2 Complexity and Rank
3 General Theory of Embeddings
4 Invariant Valuations
5 Spherical Varieties
Appendices
Bibliography
Indices
ISBN:9783642183997
Series:e-books
Series:SpringerLink (Online service)
Series:Encyclopaedia of Mathematical Sciences, 0938-0396 : v138
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups
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Call number:SPRINGER-2011-9783642172861:ONLINE Show nearby items on shelf
Title:Perspectives on Projective Geometry [electronic resource] : A Guided Tour Through Real and Complex Geometry
Author(s): Jrgen Richter-Gebert
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry.It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic andelliptic geometry or eve n relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications.In particular, itexplains how metric concepts may be best understood inprojective terms. One of the major themes that appears throughout this book is the beauty of the interplaybetweengeometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objectsand operations may be most elegantly expressed in algebraic terms, making it a va luable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the authors experience in implementinggeometric software and includes hundreds ofhigh-qualityillustrations
Note:Springer eBooks
Contents:1 Pappos's Theorem: Nine Proofs and Three Variations
2 Projective Planes
3 Homogeneous Coordinates
4 Lines and Cross
Ratios
5 Calculating with Points on Lines
6 Determinants
7 More on Bracket Algebra
8 Quadrilateral Sets and Liftings
9 Conics and Their Duals
10 Conics and Perspectivity
11 Calculating with Conics
12 Projective $d$
space
13 Diagram Techniques
14 Working with diagrams
15 Configurations, Theorems, and Bracket Expressions
16 Complex Numbers: A Primer
17 The Complex Projective Line
18 Euclidean Geometry
19 Euclidean Structures fr
ISBN:9783642172861
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algorithms , Visualization , Geometry , Discrete groups
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Call number:SPRINGER-2011-9783642156274:ONLINE Show nearby items on shelf
Title:Points and Lines [electronic resource] : Characterizing the Classical Geometries
Author(s): Ernest Shult
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphicimages of them) are c haracterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups.These tools could be useful in shortening t he enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of aLie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appealto outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such acourse, or to elicit new research directions
Note:Springer eBooks
Contents:I.Basics
1 Basics about Graphs
2 .Geometries: Basic Concepts
3 .Point
line Geometries
4.Hyperplanes, Embeddings and Teirlinck's Eheory
II.The Classical Geometries
5 .Projective Planes
6.Projective Spaces
7.Polar Spaces
8.Near Polygons
III.Methodology
9.Chamber Systems and Buildings
10.2
Covers of Chamber Systems
11.Locally Truncated Diagram Geometries
12.Separated Systems of Singular Spaces
13 Cooperstein's Theory of Symplecta and Parapolar Spaces
IV.Applications to Other Lie Incidence Geometries
15.Characterizing the Classical Strong Parapolar Spac
ISBN:9783642156274
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Geometry
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Call number:SPRINGER-2011-9783034800150:ONLINE Show nearby items on shelf
Title:Poncelet Porisms and Beyond [electronic resource] : Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics
Author(s): Vladimir Dragovi
Milena Radnovi
Date:2011
Publisher:Basel : Springer Basel
Size:1 online resource
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Note:The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, andclassical projective geomet ry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideasand their natural generalizations. Special atte ntion is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed tounderstanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems
Note:Springer eBooks
Contents:Introduction to Poncelet Porisms
Billiards First Examples
Hyper
Elliptic Curves and Their Jacobians
Projective geometry
Poncelet Theorem and Cayleys Condition
PonceletDarboux Curves and SiebeckMarden Theorem
Ellipsoidal Billiards and their Periodical Trajectories
Billiard Law and Hyper
Elliptic Curves
Poncelet Theorem and Continued Fractions
Quantum Yang
Baxter equation and (2
2)
correspondences
Bibliography
Index
ISBN:9783034800150
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic
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Call number:SPRINGER-2011-9781447121312:ONLINE Show nearby items on shelf
Title:Arithmetics [electronic resource]
Author(s): Marc Hindry
Date:2011
Publisher:London : Springer London
Size:1 online resource
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Note:Number theory is a branch of mathematics which draws its vitality from a rich historical background. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry,topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the field of theoretical computer science and in questions of communication, cryptography and error-correcting codes. Providing anelementary introduction to the central topics i n number theory, this book spans multiple areas of research. The first part corresponds to an advanced undergraduate course. All of the statements given in this part are of courseaccompanied by their proofs, with perhaps the exception of some results appe aring at the end of the chapters. A copious list of exercises, of varying difficulty, are also included here. The second part is of a higher level and isrelevant for the first year of graduate school. It contains an introduction to elliptic curves and a c hapter entitled Developments and Open Problems, which introduces and brings together various themes oriented toward ongoingmathematical research. Given the multifaceted nature of number theory, the primary aims of this book are to: - provide an overview o f the various forms of mathematics useful for studying numbers - demonstrate the necessity of deep andclassical themes such as Gauss sums - highlight the role that arithmetic plays in modern applied mathematics - include recent proofs such as the polynomi al primality algorithm - approach subjects of contemporary research such aselliptic curves - illustrate the beauty of arithmetic The prerequisites for this text are undergraduate level algebra and a little topology of Rn. It will be of use to undergraduat es, graduates and phd students, and may also appeal toprofessional mathematicians as a reference text
Note:Springer eBooks
Contents:Finite Structures
Applications: Algorithms, Primality and Factorization, Codes
Algebra and Diophantine Equations
Analytic Number Theory
Elliptic Curves
Developments and Open Problems
Factorization
Elementary Projective Geometry
Galois Theory
ISBN:9781447121312
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Field theory (Physics) , Algorithms , Number theory
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Call number:SPRINGER-2011-9781441999610:ONLINE Show nearby items on shelf
Title:Geometric Methods and Applications [electronic resource] : For Computer Science and Engineering
Author(s): Jean Gallier
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical,and applied books on c omputer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal componentanalysis, manifolds and Lie groups, quadratic optimi zation, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presentedin this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkass lemma, quadraticoptimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now incl udes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercisesthroughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: Gallier's book will be a useful source for anyone interested in applications ofgeometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications. (MathematicalReviews, 2001) ...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry. (The Australian Mathematical Society, 200 1)
Note:Springer eBooks
Contents:Introduction
Basics of Affine Geometry
Basic Properties of Convex Sets
Embedding an Affine Space in a Vector Space
Basics of Projective Geometry
Basics of Euclidean Geometry
Separating and Supporting Hyperplanes Polar Duality
Polytopes and Polyhedra
The CartanDieudonne Theorem
The Quaternions and the Spaces S3, SU(2), SO(3), and RP3
DirichletVoronoi Diagrams
Basics of Hermitian Geometry
Spectral Theorems
Singular Value Decomposition (SVD) and Polar Form
Applications of SVD and Pseudo
Inverses
Quadratic Optimization Problems
Schur
ISBN:9781441999610
Series:e-books
Series:SpringerLink (Online service)
Series:Texts in Applied Mathematics, 0939-2475 : v38
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision , Geometry , Mathematical optimization
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Call number:SPRINGER-2010-9783834897220:ONLINE Show nearby items on shelf
Title:Algebraic Geometry I [electronic resource] : Schemes With Examples and Exercises
Author(s): Ulrich Grtz
Torsten Wedhorn
Date:2010
Publisher:Wiesbaden : Vieweg+Teubner
Size:1 online resource
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Note:This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. Asystematic treatment an d motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically todiscuss the covered techniques. Thus the rea der experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check thecomprehension of the text, treat further examples, or give an ou tlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essentialfacts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local propertiesof schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes -Examples Prof. Dr. Ulrich Grtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Dep artment of Mathematics, University of Paderborn
Note:Springer eBooks
ISBN:9783834897220
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2010-9783642144417:ONLINE Show nearby items on shelf
Title:Geometry [electronic resource] : Our Cultural Heritage
Author(s): Audun Holme
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:This book contains selected topics from the history of geometry, with modern proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of futuremathematics teachers. All to o often the geometry which goes into the syllabus for these students presents the material in a pedantic and formalistic style, suppressing its dynamic character and its role as part of the foundation of ourcommon cultural heritage. As such, one of my goa ls is to open up these aspects of the field another is to extend an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledgeof mathematics are more important than ever, phrases like math avoidanc e and math anxiety are very much in the public vocabulary. Making a serious effort to heal these ills is an essential task. Thus the book also aims at an informedpublic, interested in making a new beginning in math.For the 2nd edition, some of the histori cal material giving historical context has been expanded and numerous illustrations have been added. The main difference is however theinclusion of a large number of exercises with some suggestions for solutions.For excerpts from reviews from the first ed ition have a look at http://www.springer.com/978-3-540-41949-5
Note:Springer eBooks
Contents:Part I A Cultural Heritage: 1 Early Beginnings
2 The Great River Civilizations
3 Greek and Hellenic Geometry
4 Geometry in the Hellenistic Era
5 Arabic Mathematics and Geometry
6 The Geometry of Yesterday and Today
7 Geometry and the Real World
Part II Introduction to Geometry: 8 Axiomatic Geometry
9 Axiomatic Projective Geometry
10 Models for Non
Euclidean Geometry
11 Making Things Precise
12 Projective Space
13 Geometry in the Affine and the Projective Plane
14 Algebraic Curves of Higher Degrees in the Affine Plane R2
15 Higher Geometry in the Projec
ISBN:9783642144417
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Geometry
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Call number:SPRINGER-2010-9783034602907:ONLINE Show nearby items on shelf
Title:Classification of Higher Dimensional Algebraic Varieties [electronic resource]
Author(s): Christopher D Hacon
Sndor Kovcs
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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Note:This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, itcontains a complete pro of of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to thetheory of moduli spaces. It includes topics suc h as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type. The book isaimed at advanced graduate students and researchers in algebraic geo metry
Note:Springer eBooks
Contents:I Basics
1 Introduction
2 Preliminaries
3 Singularities
3 Canonical singularities
II Recent advances in the MMP
4 Introduction
5 The main result
6 Multiplier ideal sheaves
7 Finite generation of the restricted algebra
7 Rationality of the restricted algebra
8 Log terminal models
9 Non
vanishing
10 Finiteness of log terminal models
11 Solutions and hints to some of the exercises
III Compact moduli spaces
12 Moduli problems
13 Hilbert schemes
14 The construction of the moduli space
15 Families and moduli functors
16 Subvarieties of modu
ISBN:9783034602907
Series:e-books
Series:SpringerLink (Online service)
Series:Oberwolfach Seminars : v41
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic
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Call number:SPRINGER-2010-9783034602884:ONLINE Show nearby items on shelf
Title:Affine Flag Manifolds and Principal Bundles [electronic resource]
Author(s): Alexander Schmitt
Date:2010
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Affine flag manifolds are infinite dimensional versions of familiar objects such as Gramann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid -explaining the signifi cance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamentallemma in the Langlands program), and algeb raic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book
Note:Springer eBooks
Contents:Affine Springer Fibers and Affine Deligne
Lusztig Varieties
Quantization of Hitchins Integrable System and the Geometric Langlands Conjecture
Faltings Construction of the Moduli Space of Vector Bundles on a Smooth Projective Curve
Lectures on the Moduli Stack of Vector Bundles on a Curve
On Moduli Stacks of G
bundles over a Curve
Clifford Indices for Vector Bundles on Curves
Division Algebras and Unit Groups on Surfaces
A Physics Perspective on Geometric Langlands Duality
Double Affine Hecke Algebras and Affine Flag Manifolds, I
ISBN:9783034602884
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Mathematics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic
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Call number:SPRINGER-2010-9781441991263:ONLINE Show nearby items on shelf
Title:Discrete Integrable Systems [electronic resource] : QRT Maps and Elliptic Surfaces
Author(s): J.J Duistermaat
Date:2010
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the authors insights and understanding of a birationaltransformation of the plane derived from a discrete sine-Gordon equation, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a completetreatment not only of the basic facts about QRT ma ps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodairas theory of elliptic surfaces andthe collection of nontrivial applications presented here. While prerequisit es for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able tobecome familiar with any selected interest in the book without having to make an extensive journey t hrough the literature
Note:Springer eBooks
Contents:The QRT Map
The Pencil of Biquadratic Curves in
The QRT surface
Cubic Curves in the Projective Plane
The Action of the QRT Map on Homology
Elliptic Surfaces
Automorphisms of Elliptic Surfaces
Elliptic Fibrations with a Real Structure
Rational elliptic surfaces
Symmetric QRT Maps
Examples from the Literature
Appendices
ISBN:9781441991263
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Number theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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Call number:SPRINGER-2010-9781441960535:ONLINE Show nearby items on shelf
Title:Mathematics and Its History [electronic resource]
Author(s): John Stillwell
Date:2010
Edition:3
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:From the reviews of the second edition: This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and thesolution of polynomial equation s. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topicscentral to a history course, then they would closely resem ble those chosen here. (David Parrott, Australian Mathematical Society) The book...is presented in a lively style without unnecessary detail. It is very stimulating and willbe appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interestingresults. It can be recommended for seminars and will be enjoyed by the broad mathematical community. ( European Mathematical Society) Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well asthey will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branchesof mathematics interact. (Denis Bonheure, Bulletin of the Belgian Society) This third edition includes new chapters on simple groups and combinatori cs, and new sections on several topics, including the Poincare conjecture. The bookhas also been enriched by added exercises
Note:Springer eBooks
Contents:The Theorem of Pythagoras
Greek Geometry
Greek Number Theory
Infinity in Greek Mathematics
Number Theory in Asia
Polynomial Equations
Analytic Geometry
Projective Geometry
Calculus
Infinite Series
The Number Theory Revival
Elliptic Functions
Mechanics
Complex Numbers in Algebra
Complex Numbers and Curves
Complex Numbers and Functions
Differential Geometry
Non
Euclidean Geometry
Group Theory
Hypercomplex Numbers
Algebraic Number Theory
Topology
Simple Groups
Sets, Logic, and Computation
Combinatorics
ISBN:9781441960535
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Geometry , Mathematics_$xHistory , Number theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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Call number:SPRINGER-2010-9781441904348:ONLINE Show nearby items on shelf
Title:CR Submanifolds of Complex Projective Space [electronic resource]
Author(s): Mirjana Djoric
Masafumi Okumura
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book covers the necessary topics for learning the basic properties of complex manifolds and their submanifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader totopics of current research and to more advanced publications. The book begins with an introduction to the geometry of complex manifolds and their submanifolds and describes the properties of hypersurfaces and CR submanifolds, withparticular emphasis on CR submanifolds of maximal CR dimension. The second part contains results which are not new, but recently published in some mathematical journals. The final part contains several original results by the authors,with complete proofs. Key features of CR Submanifolds of Complex Projecti ve Space: - Presents recent developments and results in the study of submanifolds previously published only in research papers. - Special topics exploredinclude: the Khler manifold, submersion and immersion, codimension reduction of a submanifold, tubes o ver submanifolds, geometry of hypersurfaces and CR submanifolds of maximal CR dimension. - Provides relevant techniques, resultsand their applications, and presents insight into the motivations and ideas behind the theory. - Presents the fundamental defin itions and results necessary for reaching the frontiers of research in this field. This text is largelyself-contained. Prerequisites include basic knowledge of introductory manifold theory and of curvature properties of Riemannian geometry. Advanced under graduates, graduate students and researchers in differential geometry will benefitfrom this concise approach to an important topic
Note:Springer eBooks
Contents:1. Complex manifold
2. Almost complex structure
3. Complex vector space complexification
4. Khler manifold
5. Structure equations of a submanifold
6. Submanifolds of a Euclidean space
7. Submanifolds of a complex manifold
8. The Levi form
9. The principal circle bundle S^{2n+1}({\bf P}^n({\bf C}),S^1)
10. Submersion and immersion
11. Hypersurfaces of a Riemannian manifold of constant curvature
12. Hypersurfaces of a sphere S^{n+1}(1/a)
13. Hypersurfaces of a sphere with parallel shape operator
14. Codimension reduction of a submanifold
15. CR submani
ISBN:9781441904348
Series:e-books
Series:SpringerLink (Online service)
Series:Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt, 1389-2177 : v19
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2010-9780857290601:ONLINE Show nearby items on shelf
Title:Worlds Out of Nothing [electronic resource] : A Course in the History of Geometry in the 19th Century
Author(s): Jeremy Gray
Date:2010
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students inmathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was itappreciated? What new questions did it generate? Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singularpoints of algebraic curves (Plckers equations) and their role in resolving a p aradox in the theory of duality to Riemanns work on differential geometry and to Beltramis role in successfully establishing non-Euclideangeometry as a rigorous mathematical subject. The final part of the book considers how projective geometry, as exempli fied by Kleins Erlangen Program, rose to prominence, and looks at Poincars ideas about non-Euclidean geometryand their physical and philosophical significance. It then concludes with discussions on geometry and formalism, examining the Italian contributio n and Hilberts Foundations of Geometry geometry and physics, with a look at some ofEinsteins ideas and geometry and truth. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the sub ject, advice on how to write essays, and comments on whatinstructors should be looking for
Note:Springer eBooks
Contents:Mathematics in the French Revolution
Poncelet (and Pole and Polar)
Theorems in Projective Geometry
Poncelets Trait
Duality and the Duality Controversy
Poncelet, Chasles, and the Early Years of Projective Geometry
Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre
Gauss (Schweikart and Taurinus) and Gausss Differential Geometry
Jnos Bolyai
Lobachevskii
Publication and Non
Reception up to 1855
On Writing the History of Geometry 1
Across the Rhine Mbiuss Algebraic Version of Projective Geometry
Plcker, H
ISBN:9780857290601
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Mathematics_$xHistory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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Call number:SPRINGER-2010-9780817649135:ONLINE Show nearby items on shelf
Title:Hyperbolic Manifolds and Discrete Groups [electronic resource]
Author(s): Michael Kapovich
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is onThurstons hyperbolization t heorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to thehyperbolization theorem as well as rich discussions on related t opics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich setof examples, numerous exercises, and an extensive bibliography and index, Hyperbolic M anifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairlyself-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem,this is an important book which had to be written some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolizationtheorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. -- -Zentralbatt MATH This book can act as source material for a postgraduatecourse and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide
Note:Springer eBooks
Contents:Preface
Three
dimensional Topology
Thurston Norm
Geometry of the Hyperbolic Space
Kleinian Groups
Teichmller Theory of Riemann Surfaces
Introduction to the Orbifold Theory
Complex Projective Structures
Sociology of Kleinian Groups
Ultralimits of Metric Spaces
Introduction to Group Actions on Trees
Laminations, Foliations and Trees
Rips Theory
Brooks' Theorem and Circle Packings
Pleated Surfaces and Ends of Hyperbolic Manifolds
Outline of the Proof of the Hyperbolization Theorem
Reduction to The Bounded Image Theorem
The Bounded Image Theorem
ISBN:9780817649135
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Geometry , Topology , Cell aggregation Mathematics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
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Call number:SPRINGER-2010-9780387729237:ONLINE Show nearby items on shelf
Title:Discrete Integrable Systems [electronic resource] : QRT Maps and Elliptic Surfaces
Author(s): J.J Duistermaat
Date:2010
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the authors insights and understanding of a birationaltransformation of the plane derived from a discrete sine-Gordon equation, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a completetreatment not only of the basic facts about QRT ma ps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodairas theory of elliptic surfaces andthe collection of nontrivial applications presented here. While prerequisit es for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able tobecome familiar with any selected interest in the book without having to make an extensive journey t hrough the literature
Note:Springer eBooks
Contents:The QRT Map
The Pencil of Biquadratic Curves in
The QRT surface
Cubic Curves in the Projective Plane
The Action of the QRT Map on Homology
Elliptic Surfaces
Automorphisms of Elliptic Surfaces
Elliptic Fibrations with a Real Structure
Rational elliptic surfaces
Symmetric QRT Maps
Examples from the Literature
Appendices
ISBN:9780387729237
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382 : v304
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Functions of complex variables , Number theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
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