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Author : Steve Bradlow
Release : 2009-05-21
Genre : Mathematics
Kind : eBook
Book Rating : 711/5 ( reviews)
Book Synopsis Moduli Spaces and Vector Bundles by : Steve Bradlow
Download or read book Moduli Spaces and Vector Bundles written by Steve Bradlow. This book was released on 2009-05-21. Available in PDF, EPUB and Kindle. Book excerpt: Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Author : Leticia Brambila-Paz
Release : 2009-05-21
Genre : Mathematics
Kind : eBook
Book Rating : 049/5 ( reviews)
Book Synopsis Moduli Spaces and Vector Bundles by : Leticia Brambila-Paz
Download or read book Moduli Spaces and Vector Bundles written by Leticia Brambila-Paz. This book was released on 2009-05-21. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Christian Okonek
Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 602/5 ( reviews)
Book Synopsis Vector Bundles on Complex Projective Spaces by : Christian Okonek
Download or read book Vector Bundles on Complex Projective Spaces written by Christian Okonek. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Daniel Huybrechts
Release : 2010-05-27
Genre : Mathematics
Kind : eBook
Book Rating : 822/5 ( reviews)
Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts
Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts. This book was released on 2010-05-27. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Robert Friedman
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)
Book Synopsis Algebraic Surfaces and Holomorphic Vector Bundles by : Robert Friedman
Download or read book Algebraic Surfaces and Holomorphic Vector Bundles written by Robert Friedman. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.
