Algebraic Varieties


Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Category: Mathematics
Page: 163
View: 9306

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An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Vector Bundles in Algebraic Geometry


Author: N. J. Hitchin,P. E. Newstead,W. M. Oxbury
Publisher: Cambridge University Press
ISBN: 9780521498784
Category: Mathematics
Page: 345
View: 9652

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The study of vector bundles over algebraic varieties has been stimulated over the last few years by successive waves of migrant concepts, largely from mathematical physics, whilst retaining its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on Vector Bundles in Algebraic Geometry brought together some of the leading researchers in the field to explore further these interactions. This book is a collection of survey articles by the main speakers at the symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles. Topics covered include those linking gauge theory and geometric invariant theory such as augmented bundles and coherent systems; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal field theory and the moduli spaces of bundles on curves; the Horrocks–Mumford bundle and codimension 2 subvarieties in P4 and P5; exceptional bundles and stable sheaves on projective space.

Algebraic and Analytic Geometry


Author: Amnon Neeman
Publisher: Cambridge University Press
ISBN: 0521709830
Category: Mathematics
Page: 420
View: 9746

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Modern introduction to algebraic geometry for undergraduates; uses analytic ideas to access algebraic theory.

Number Theory and Algebraic Geometry


Author: Miles Reid,H. P. F. Swinnerton-Dyer,Alexei Skorobogatov
Publisher: Cambridge University Press
ISBN: 9780521545181
Category: Mathematics
Page: 300
View: 3055

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This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

Algebraic Topology Via Differential Geometry


Author: M. Karoubi,C. Leruste
Publisher: Cambridge University Press
ISBN: 9780521317146
Category: Mathematics
Page: 363
View: 3249

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In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

Algebraic Cycles and Motives:


Author: Jan Nagel,Chris Peters
Publisher: Cambridge University Press
ISBN: 0521701740
Category: Mathematics
Page: 292
View: 9572

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This 2007 book is a self-contained account of the subject of algebraic cycles and motives.

O-Minimality and Diophantine Geometry


Author: A. J. Wilkie,G. O. Jones
Publisher: Cambridge University Press
ISBN: 1107462495
Category: Mathematics
Page: 232
View: 7585

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Brings the researcher up to date with recent applications of mathematical logic to number theory.

Geometry of Low-Dimensional Manifolds: Volume 2

Symplectic Manifolds and Jones-Witten Theory
Author: Donaldson/Thomas,London Mathematical Society
Publisher: Cambridge University Press
ISBN: 9780521400015
Category: Mathematics
Page: 260
View: 9901

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These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.

Lectures on Invariant Theory


Author: Igor Dolgachev
Publisher: Cambridge University Press
ISBN: 9780521525480
Category: Mathematics
Page: 220
View: 447

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The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Applicable Differential Geometry


Author: Mike Crampin,M. Crampin,N. Crampin,F. A. E. Pirani,Pirani F A E
Publisher: Cambridge University Press
ISBN: 9780521231909
Category: Mathematics
Page: 394
View: 7080

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An introduction to geometrical topics used in applied mathematics and theoretical physics.

Moduli Spaces


Author: L. Brambila,Peter Newstead,Richard P. Thomas,Oscar García-Prada
Publisher: Cambridge University Press
ISBN: 1107636388
Category: Mathematics
Page: 346
View: 5680

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A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

Synthetic Differential Geometry


Author: Anders Kock
Publisher: Cambridge University Press
ISBN: 0521687381
Category: Mathematics
Page: 233
View: 5809

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Second edition of this book detailing how limit processes can be represented algebraically.

Arithmetic of Blowup Algebras


Author: Wolmer V. Vasconcelos
Publisher: Cambridge University Press
ISBN: 9780521454841
Category: Mathematics
Page: 329
View: 3172

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This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.

Sheaf Theory


Author: B. R. Tennison
Publisher: Cambridge University Press
ISBN: 0521207843
Category: Mathematics
Page: 164
View: 5740

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Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based on a lecture course for graduate pure mathematicians which builds up enough of the foundations of sheaf theory to give a broad definition of manifold, covering as special cases the algebraic geometer's schemes as well as the topological, differentiable and analytic kinds, and to define sheaf cohomology for application to such objects. Exercises are provided at the end of each chapter and at various places in the text. Hints and solutions to some of them are given at the end of the book.

The Grothendieck Theory of Dessins D'Enfants


Author: Leila Schneps
Publisher: Cambridge University Press
ISBN: 9780521478212
Category: Mathematics
Page: 368
View: 6308

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The various articles here unite all of the basics of the study of dessins d'enfants as well as the most recent advances.

Groups and Geometry


Author: Roger C. Lyndon
Publisher: Cambridge University Press
ISBN: 0521316944
Category: Mathematics
Page: 217
View: 9664

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This 1985 book is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and leads the reader to the frontiers of current research at the time of publication.

Recent Advances in Algebraic Geometry


Author: Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Publisher: Cambridge University Press
ISBN: 110764755X
Category: Mathematics
Page: 447
View: 1202

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A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces


Author: S. K. Donaldson,S. Donaldson,C. B. Thomas
Publisher: Cambridge University Press
ISBN: 9780521399784
Category: Mathematics
Page: 276
View: 6041

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Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.