Topological Methods in Algebraic Geometry

Reprint of the 1978 Edition

  • Friedrich Hirzebruch

Part of the Classics in Mathematics book series (volume 131)

Table of contents

  1. Front Matter
    Pages ins1-XI
  2. Friedrich Hirzebruch
    Pages 1-8
  3. Friedrich Hirzebruch
    Pages 8-75
  4. Friedrich Hirzebruch
    Pages 76-90
  5. Friedrich Hirzebruch
    Pages 91-113
  6. Friedrich Hirzebruch
    Pages 114-158
  7. Back Matter
    Pages 159-234

About this book

Introduction

In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for­ mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo­ morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954.

Keywords

Characteristic class Riemann-Roch theorem algebraic varieties cohomology corbordism ring homology todd genus topological methods vector bundle

Authors and affiliations

  • Friedrich Hirzebruch
    • 1
    • 2
  1. 1.Max-Planck-Institut für MathematikBonnGermany
  2. 2.Mathematisches InstitutUniversität BonnBonnWest Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-62018-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58663-0
  • Online ISBN 978-3-642-62018-8
  • Series Print ISSN 0072-7830
  • About this book