Vector Bundles

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Vector Bundles and Their Applications

Glenys Luke,Alexander S. Mishchenko
Vector Bundles and Their Applications Book PDF

Author : Glenys Luke,Alexander S. Mishchenko
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 48,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475769234

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Vector Bundles and Their Applications by Glenys Luke,Alexander S. Mishchenko Pdf

The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.

Algebraic Surfaces and Holomorphic Vector Bundles

Robert Friedman
Algebraic Surfaces and Holomorphic Vector Bundles Book PDF

Author : Robert Friedman
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461216889

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Algebraic Surfaces and Holomorphic Vector Bundles by Robert Friedman Pdf

A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.

Characteristic Classes

John Willard Milnor,James D. Stasheff
Characteristic Classes Book PDF

Author : John Willard Milnor,James D. Stasheff
Publisher : Princeton University Press
Page : 342 pages
File Size : 49,5 Mb
Release : 1974
Category : Mathematics
ISBN : 0691081220

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Characteristic Classes by John Willard Milnor,James D. Stasheff Pdf

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Vector Bundles - Vol 1

Anonim
Vector Bundles Vol 1 Book PDF

Author : Anonim
Publisher : Academic Press
Page : 370 pages
File Size : 52,7 Mb
Release : 1983-02-18
Category : Mathematics
ISBN : 0080874207

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Vector Bundles - Vol 1 by Anonim Pdf

Vector Bundles - Vol 1

Differential Geometry of Complex Vector Bundles

Shoshichi Kobayashi
Differential Geometry of Complex Vector Bundles Book PDF

Author : Shoshichi Kobayashi
Publisher : Princeton University Press
Page : 317 pages
File Size : 50,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400858682

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Differential Geometry of Complex Vector Bundles by Shoshichi Kobayashi Pdf

Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Vector Bundles on Complex Projective Spaces

Christian Okonek,Heinz Spindler,Michael Schneider
Vector Bundles on Complex Projective Spaces Book PDF

Author : Christian Okonek,Heinz Spindler,Michael Schneider
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 51,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475714609

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Vector Bundles on Complex Projective Spaces by Christian Okonek,Heinz Spindler,Michael Schneider Pdf

These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.

Vector Bundles in Algebraic Geometry

N. J. Hitchin
Vector Bundles in Algebraic Geometry Book PDF

Author : N. J. Hitchin
Publisher : Cambridge University Press
Page : 359 pages
File Size : 55,9 Mb
Release : 1995-03-16
Category : Mathematics
ISBN : 9780521498784

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Vector Bundles in Algebraic Geometry by N. J. Hitchin Pdf

This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.

Cohomology of Vector Bundles and Syzygies

Jerzy Weyman
Cohomology of Vector Bundles and Syzygies Book PDF

Author : Jerzy Weyman
Publisher : Cambridge University Press
Page : 404 pages
File Size : 47,9 Mb
Release : 2003-06-09
Category : Mathematics
ISBN : 0521621976

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Cohomology of Vector Bundles and Syzygies by Jerzy Weyman Pdf

The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

Vector Bundles on Complex Projective Spaces

Christian Okonek,Michael Schneider,Heinz Spindler
Vector Bundles on Complex Projective Spaces Book PDF

Author : Christian Okonek,Michael Schneider,Heinz Spindler
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 50,6 Mb
Release : 2011-07-07
Category : Mathematics
ISBN : 9783034801508

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Vector Bundles on Complex Projective Spaces by Christian Okonek,Michael Schneider,Heinz Spindler Pdf

These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S ́eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G ̈ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of pa- graphs. Each section is preceded by a short description of its contents.

Moduli Spaces and Vector Bundles

Steve Bradlow
Moduli Spaces and Vector Bundles Book PDF

Author : Steve Bradlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 45,5 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780521734714

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Moduli Spaces and Vector Bundles by Steve Bradlow Pdf

Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Algebraic Surfaces and Holomorphic Vector Bundles

Robert Friedman
Algebraic Surfaces and Holomorphic Vector Bundles Book PDF

Author : Robert Friedman
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 53,9 Mb
Release : 1998-01-23
Category : Mathematics
ISBN : 0387983619

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Algebraic Surfaces and Holomorphic Vector Bundles by Robert Friedman Pdf

A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.

Lectures on Vector Bundles

J. Le Potier
Lectures on Vector Bundles Book PDF

Author : J. Le Potier
Publisher : Cambridge University Press
Page : 260 pages
File Size : 49,6 Mb
Release : 1997-01-28
Category : Mathematics
ISBN : 0521481821

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Lectures on Vector Bundles by J. Le Potier Pdf

This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Helices and Vector Bundles

A. N. Rudakov
Helices and Vector Bundles Book PDF

Author : A. N. Rudakov
Publisher : Cambridge University Press
Page : 153 pages
File Size : 51,8 Mb
Release : 1990-07-12
Category : Mathematics
ISBN : 9780521388115

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Helices and Vector Bundles by A. N. Rudakov Pdf

Arising out of a series of seminars organized in Moscow by A.N. Rudakov, this volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry.

Vector Bundles and Representation Theory

Steven Dale Cutkosky
Vector Bundles and Representation Theory Book PDF

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 41,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832646

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Vector Bundles and Representation Theory by Steven Dale Cutkosky Pdf

This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Vector Bundles and Complex Geometry

Oscar García-Prada
Vector Bundles and Complex Geometry Book PDF

Author : Oscar García-Prada
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 43,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821847503

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Vector Bundles and Complex Geometry by Oscar García-Prada Pdf

This volume contains a collection of papers from the Conference on Vector Bundles held at Miraflores de la Sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, Hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.