Algebraic Varieties


Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Category: Mathematics
Page: 163
View: 7469

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

Algebraic and Analytic Geometry


Author: Amnon Neeman
Publisher: Cambridge University Press
ISBN: 0521709830
Category: Mathematics
Page: 420
View: 7503

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

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: 9851

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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 Topology Via Differential Geometry


Author: M. Karoubi,C. Leruste
Publisher: Cambridge University Press
ISBN: 9780521317146
Category: Mathematics
Page: 363
View: 6102

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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: 1246

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

Lectures on Invariant Theory


Author: Igor Dolgachev
Publisher: Cambridge University Press
ISBN: 9780521525480
Category: Mathematics
Page: 220
View: 8752

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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.

Geometric and Cohomological Group Theory


Author: Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis
Publisher: Cambridge University Press
ISBN: 131662322X
Category: Mathematics
Page: 278
View: 2735

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Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

Synthetic Differential Geometry


Author: Anders Kock
Publisher: Cambridge University Press
ISBN: 0521687381
Category: Mathematics
Page: 233
View: 1312

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

Geometry of Riemann Surfaces


Author: Frederick P. Gardiner,Gabino González-Diez,Christos Kourouniotis
Publisher: Cambridge University Press
ISBN: 0521733073
Category: Mathematics
Page: 395
View: 5393

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Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, conformal dynamics, discrete groups, algebraic curves and more. This collection of articles presents original research and expert surveys of important related topics, making the field accessible to research workers, graduate students and teachers.

Recent Advances in Algebraic Geometry


Author: Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Publisher: Cambridge University Press
ISBN: 110764755X
Category: Mathematics
Page: 447
View: 9230

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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

Proceedings of the Durham Symposium, July 1989
Author: S. K. Donaldson,Charles Benedict Thomas
Publisher: Cambridge University Press
ISBN: 9780521400015
Category: Low-dimensional topology
Page: 242
View: 6619

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Applicable Differential Geometry


Author: M. Crampin,F. A. E. Pirani
Publisher: Cambridge University Press
ISBN: 9780521231909
Category: Mathematics
Page: 394
View: 3588

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

Sheaf Theory


Author: B. R. Tennison
Publisher: Cambridge University Press
ISBN: 0521207843
Category: Mathematics
Page: 164
View: 3956

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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.

O-Minimality and Diophantine Geometry


Author: A. J. Wilkie,G. O. Jones
Publisher: Cambridge University Press
ISBN: 1107462495
Category: Mathematics
Page: 232
View: 3510

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

Groups and Geometry


Author: Roger C. Lyndon
Publisher: Cambridge University Press
ISBN: 0521316944
Category: Mathematics
Page: 217
View: 650

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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.

Topological Methods in Group Theory


Author: Ross Geoghegan
Publisher: Springer Science & Business Media
ISBN: 0387746110
Category: Mathematics
Page: 473
View: 5739

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This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

The Grothendieck Theory of Dessins D'Enfants


Author: Leila Schneps
Publisher: Cambridge University Press
ISBN: 9780521478212
Category: Mathematics
Page: 368
View: 4053

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Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.

Introduction to Operator Space Theory


Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 9780521811651
Category: Mathematics
Page: 478
View: 2837

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An introduction to the theory of operator spaces, emphasising applications to C*-algebras.