Vector Bundles on Complex Projective Spaces: With an Appendix by S. I. Gelfand / Edition 1

by Christian Okonek, Michael Schneider, Heinz Spindler

Overview

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 = P . According to Serre (GAGA) the class- n cation 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 fundamental results from these fields are summarized at the beginning. One of the authors gave a survey in the S´eminaire Bourbaki 1978 on the current state of the classification 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 difficult 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.

Product Details

ISBN-13:	9783034801508
Publisher:	Springer Basel
Publication date:	07/08/2011
Series:	Modern Birkh�user Classics
Edition description:	1980
Pages:	239
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

Christian Okonek is Professor for mathematics at the University of Zurich. Michael Schneider was Professor for algebraic geometry at the University of Bayreuth, deceased in 1997. Heinz Spindler is Professor for mathematics at the University of Osnabrück.

Table of Contents

Introduction.- Chapter 1. Holomorphic vector bundles and the geometry of Pn.- Chapter 2. Stability and moduli spaces.- Bibliography.- Supplemental Bibliography.- Index.- Appendix A. Sheaves on Pn and problems in linear algebra.- Bibliography for Appendix A.