Algebraic Varieties


Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Category: Mathematics
Page: 163
View: 3884

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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: 8900

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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.

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: 6912

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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.

Algebraic Geometry

A Concise Dictionary
Author: Elena Rubei
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110316234
Category: Mathematics
Page: 239
View: 4093

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Algebraic geometry has a complicated, difficult language. This book contains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of related subjects are included. It helps beginners that know some, but not all, basic facts of algebraic geometry to follow seminars and to read papers. The dictionary form makes it easy and quick to consult.

New Trends in Algebraic Geometry


Author: K. Hulek
Publisher: Cambridge University Press
ISBN: 9780521646598
Category: Mathematics
Page: 484
View: 333

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Seventeen articles from the most outstanding contemporary topics in algebraic geometry.

Galois Representations in Arithmetic Algebraic Geometry


Author: A. J. Scholl,R. L. Taylor,Robert L. Taylor
Publisher: Cambridge University Press
ISBN: 9780521644198
Category: Mathematics
Page: 493
View: 7960

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Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

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: 2981

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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.

Linear Algebraic Monoids


Author: Mohan S. Putcha
Publisher: Cambridge University Press
ISBN: 0521358094
Category: Mathematics
Page: 171
View: 2418

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This book provides an introduction to the field of linear algebraic monoids. This subject represents a synthesis of ideas from the theory of algebraic groups, algebraic geometry, matrix theory and abstract semigroup theory. Since every representation of an algebraic group gives rise to an algebraic monoid, the objects of study do indeed arise naturally.

Recent Advances in Algebraic Geometry


Author: Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Publisher: Cambridge University Press
ISBN: 110764755X
Category: Mathematics
Page: 447
View: 1196

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

Quadratic Forms with Applications to Algebraic Geometry and Topology


Author: Albrecht Pfister
Publisher: Cambridge University Press
ISBN: 9780521467551
Category: Mathematics
Page: 179
View: 9725

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This volume discusses results about quadratic forms that give rise to interconnections among number theory, algebra, algebraic geometry, and topology. The author deals with various topics including Hilbert's 17th problem, the Tsen-Lang theory of quasi-algebraically closed fields, the level of topological spaces, and systems of quadratic forms over arbitrary fields. Whenever possible, proofs are short and elegant, and the author has made this book as self-contained as possible. This book brings together thirty years' worth of results certain to interest anyone whose research touches on quadratic forms.

Cox Rings


Author: Ivan Arzhantsev,Ulrich Derenthal,Jürgen Hausen,Antonio Laface
Publisher: Cambridge University Press
ISBN: 1107024625
Category: Mathematics
Page: 472
View: 6404

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This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

The Resolution of Singular Algebraic Varieties


Author: David Ellwood,Herwig Hauser,Shigefumi Mori,Josef Schicho
Publisher: American Mathematical Soc.
ISBN: 0821889826
Category: Mathematics
Page: 340
View: 4981

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Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Number Theory


Author: Seminaire De Theorie Des Nombres De Paris (1993-1994)
Publisher: Cambridge University Press
ISBN: 9780521585491
Category: Mathematics
Page: 213
View: 2055

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This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide.

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: 7768

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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.

Algebraic Topology

A Student's Guide
Author: J. F. Adams
Publisher: Cambridge University Press
ISBN: 9780521080767
Category: Mathematics
Page: 300
View: 1251

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This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the second part of the book comprises a collection of some of these classic expositions, from journals, lecture notes, theses and conference proceedings. They are connected by short explanatory passages written by Professor Adams, whose own contributions to this branch of mathematics are represented in the reprinted articles.