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| Author | : Steve Bradlow |
| Publisher | : Cambridge University Press |
| Total Pages | : 516 |
| Release | : 2009-05-21 |
| Genre | : Mathematics |
| ISBN | : 0521734711 |
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
| Author | : P. E. Newstead |
| Publisher | : Alpha Science International Limited |
| Total Pages | : 166 |
| Release | : 2012 |
| Genre | : 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 | : Robert Friedman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2012-12-06 |
| Genre | : 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 | : Masaki Maruyama |
| Publisher | : CRC Press |
| Total Pages | : 324 |
| Release | : 2023-05-31 |
| Genre | : Mathematics |
| ISBN | : 1000950700 |
"Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."
| Author | : Daniel Huybrechts |
| Publisher | : Cambridge University Press |
| Total Pages | : 345 |
| Release | : 2010-05-27 |
| Genre | : 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 |
| Total Pages | : 399 |
| Release | : 2013-11-11 |
| Genre | : 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 | : J. Le Potier |
| Publisher | : Cambridge University Press |
| Total Pages | : 260 |
| Release | : 1997-01-28 |
| Genre | : 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.
| Author | : N. J. Hitchin |
| Publisher | : Cambridge University Press |
| Total Pages | : 359 |
| Release | : 1995-03-16 |
| Genre | : 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 | : Shoshichi Kobayashi |
| Publisher | : Princeton University Press |
| Total Pages | : 317 |
| Release | : 2014-07-14 |
| Genre | : 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 | : Alfonso Zamora Saiz |
| Publisher | : Springer Nature |
| Total Pages | : 127 |
| Release | : 2021-03-24 |
| Genre | : Mathematics |
| ISBN | : 3030678296 |
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
