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Vector Bundles on Complex Projective Spaces

  • Book
  • © 1980

Overview

Authors:
  1. Christian Okonek

    1. Mathematische Institut der Universität, Göttingen, Federal Republic of Germany

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  2. Michael Schneider

    1. Mathematische Institut der Universität, Göttingen, Federal Republic of Germany

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  3. Heinz Spindler

    1. Mathematische Institut der Universität, Göttingen, Federal Republic of Germany

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

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Table of contents (2 chapters)

  1. Front Matter

    Pages N1-vii
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  2. Holomorphic Vector Bundles and the Geometry of ℙn

    • Christian Okonek, Michael Schneider, Heinz Spindler
    Pages 1-138

  3. Stability and Moduli Spaces

    • Christian Okonek, Michael Schneider, Heinz Spindler
    Pages 139-373

  4. Back Matter

    Pages 374-389
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematische Institut der Universität, Göttingen, Federal Republic of Germany

    Christian Okonek, Michael Schneider, Heinz Spindler

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