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Algebraic Surfaces and Holomorphic Vector Bundles

  • Textbook
  • © 1998

Overview

Authors:
  1. Robert Friedman

    1. Department of Mathematics, Columbia University, New York, USA

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  • One of the books primary assets is its method of presentation which makes the subject rather accessible
  • The only prerequisite is a good working knowledge of elementary algebraic geometry
  • Unified introduction to the study of algebraic surfaces and vector bundles
  • Algebraic geometry is an active area of current research

Part of the book series: Universitext (UTX)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Robert Friedman
    Pages 1-5

  3. Curves on a Surface

    • Robert Friedman
    Pages 7-24

  4. Coherent Sheaves

    • Robert Friedman
    Pages 25-58

  5. Birational Geometry

    • Robert Friedman
    Pages 59-83

  6. Stability

    • Robert Friedman
    Pages 85-112

  7. Some Examples of Surfaces

    • Robert Friedman
    Pages 113-139

  8. Vector Bundles over Ruled Surfaces

    • Robert Friedman
    Pages 141-165

  9. An Introduction to Elliptic Surfaces

    • Robert Friedman
    Pages 167-195

  10. Vector Bundles over Elliptic Surfaces

    • Robert Friedman
    Pages 197-243

  11. Bogomolov’s Inequality and Applications

    • Robert Friedman
    Pages 245-276

  12. Classification of Algebraic Surfaces and of Stable Bundles

    • Robert Friedman
    Pages 277-314

  13. Back Matter

    Pages 315-328
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Keywords

About this book

This book is based on courses given at Columbia University on vector bun­ dles (1988) and on the theory of algebraic surfaces (1992), as well as lectures in the Park City lIAS Mathematics Institute on 4-manifolds and Donald­ son invariants. The goal of these lectures was to acquaint researchers in 4-manifold topology with the classification of algebraic surfaces and with methods for describing moduli spaces of holomorphic bundles on algebraic surfaces with a view toward computing Donaldson invariants. Since that time, the focus of 4-manifold topology has shifted dramatically, at first be­ cause topological methods have largely superseded algebro-geometric meth­ ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim­ the new invariants defined by Seiberg plified the theory and led to proofs of the basic conjectures concerning the 4-manifold topology of algebraic surfaces. However, the study of algebraic surfaces and the moduli spaces ofbundles on them remains a fundamen­ tal problem in algebraic geometry, and I hope that this book will make this subject more accessible. Moreover, the recent applications of Seiberg­ Witten theory to symplectic 4-manifolds suggest that there is room for yet another treatment of the classification of algebraic surfaces. In particular, despite the number of excellent books concerning algebraic surfaces, I hope that the half of this book devoted to them will serve as an introduction to the subject.

Authors and Affiliations

  • Department of Mathematics, Columbia University, New York, USA

    Robert Friedman

Bibliographic Information

  • Book Title: Algebraic Surfaces and Holomorphic Vector Bundles

  • Authors: Robert Friedman

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-1688-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98361-5Published: 23 January 1998

  • Softcover ISBN: 978-1-4612-7246-5Published: 08 October 2012

  • eBook ISBN: 978-1-4612-1688-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: IX, 329

  • Topics: Algebraic Geometry

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