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Vector Bundles on Complex Projective Spaces

  • Christian Okonek
  • Michael Schneider
  • Heinz Spindler

Part of the Progress in Mathematics book series (PM, volume 3)

Table of contents

  1. Front Matter
    Pages N1-vii
  2. Christian Okonek, Michael Schneider, Heinz Spindler
    Pages 1-138
  3. Christian Okonek, Michael Schneider, Heinz Spindler
    Pages 139-373
  4. Back Matter
    Pages 374-389

About this book

Introduction

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.

Keywords

algebra algebraic geometry geometry Manifold theorem

Authors and affiliations

  • Christian Okonek
    • 1
  • Michael Schneider
    • 1
  • Heinz Spindler
    • 1
  1. 1.Mathematische Institut der UniversitätGöttingenFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1460-9
  • Copyright Information Springer-Verlag US 1980
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-1462-3
  • Online ISBN 978-1-4757-1460-9
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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