Universitext

Algebraic Surfaces and Holomorphic Vector Bundles

Authors: Friedman, Robert

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About this Textbook

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time, the focus of 4-manifold topology has shifted dramatically, at first be­ cause topological methods have largely superseded algebro-geometric meth­ ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim­ the new invariants defined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 of bundles 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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-1-4612-1688-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
Softcover $79.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Surfaces and Holomorphic Vector Bundles
Authors
Series Title
Universitext
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1688-9
DOI
10.1007/978-1-4612-1688-9
Hardcover ISBN
978-0-387-98361-5
Softcover ISBN
978-1-4612-7246-5
Series ISSN
0172-5939
Edition Number
1
Number of Pages
IX, 329
Topics