Several Complex Variables VII

Sheaf-Theoretical Methods in Complex Analysis

  • H. Grauert
  • Th. Peternell
  • R. Remmert

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 74)

Table of contents

  1. Front Matter
    Pages i-viii
  2. H. Grauert, Th. Peternell, R. Remmert
    Pages 1-5
  3. R. Remmert
    Pages 7-96
  4. Th. Peternell
    Pages 145-182
  5. G. Dethloff, H. Grauert
    Pages 183-220
  6. H. Grauert
    Pages 259-284
  7. Th. Peternell
    Pages 285-317
  8. F. Campana, Th. Peternell
    Pages 319-349
  9. H. Grauert, R. Remmert
    Pages 351-360
  10. Back Matter
    Pages 361-372

About this book

Introduction

Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g­ dimensional complex torus to X. If 9 ~ 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, ... , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.

Keywords

Complex analysis Complex spaces Kohomologie Kohärente Garben Konvexität und Konkavität Modifikation Pseudoconvexity calculus coherent sheaves cohomology convexity and concavity komplexe Räume modifications

Editors and affiliations

  • H. Grauert
    • 1
  • Th. Peternell
    • 2
  • R. Remmert
    • 3
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Mathematisches InstitutUniversität BayreuthBayreuthGermany
  3. 3.Mathematisches InstitutUniversität MünsterMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-09873-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08150-7
  • Online ISBN 978-3-662-09873-8
  • Series Print ISSN 0938-0396
  • About this book