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Author : Steve Bradlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 15,10 MB
Release : 2009-05-21
Category : Mathematics
ISBN : 0521734711
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Author : Leticia Brambila-Paz
Publisher : Cambridge University Press
Page : 506 pages
File Size : 35,78 MB
Release : 2009-05-21
Category : Mathematics
ISBN : 1139480049
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 345 pages
File Size : 17,90 MB
Release : 2010-05-27
Category : Mathematics
ISBN : 1139485822
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Author : Christian Okonek
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 36,9 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 1475714602
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.
Author :
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 19,55 MB
Release :
Category :
ISBN : 0821883763
Author : Robert Friedman
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 25,58 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461216885
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.
Author : N. J. Hitchin
Publisher : Cambridge University Press
Page : 359 pages
File Size : 32,68 MB
Release : 1995-03-16
Category : Mathematics
ISBN : 0521498783
This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.
Author : P. E. Newstead
Publisher : Alpha Science International Limited
Page : 166 pages
File Size : 44,89 MB
Release : 2012
Category : Mathematics
ISBN : 9788184871623
Geometric Invariant Theory (GIT), developed in the 1960s by David Mumford, is the theory of quotients by group actions in Algebraic Geometry. Its principal application is to the construction of various moduli spaces. Peter Newstead gave a series of lectures in 1975 at the Tata Institute of Fundamental Research, Mumbai on GIT and its application to the moduli of vector bundles on curves. It was a masterful yet easy to follow exposition of important material, with clear proofs and many examples. The notes, published as a volume in the TIFR lecture notes series, became a classic, and generations of algebraic geometers working in these subjects got their basic introduction to this area through these lecture notes. Though continuously in demand, these lecture notes have been out of print for many years. The Tata Institute is happy to re-issue these notes in a new print.
Author : Shoshichi Kobayashi
Publisher : Princeton University Press
Page : 317 pages
File Size : 35,29 MB
Release : 2014-07-14
Category : Mathematics
ISBN : 1400858682
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.
Author : J. Le Potier
Publisher : Cambridge University Press
Page : 260 pages
File Size : 16,86 MB
Release : 1997-01-28
Category : Mathematics
ISBN : 9780521481823
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.