Local Moduli and Singularities

  • Authors
  • Olav Arnfinn Laudal
  • Gerhard Pfister

Part of the Lecture Notes in Mathematics book series (LNM, volume 1310)

Table of contents

  1. Front Matter
    Pages I-V
  2. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 1-7
  3. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 8-14
  4. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 15-31
  5. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 32-60
  6. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 61-71
  7. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 72-87
  8. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 88-104
  9. Olav Arnfinn Laudal, Gerhard Pfister
    Pages 105-111
  10. Back Matter
    Pages 112-117

About this book

Introduction

This research monograph sets out to study the notion of a local moduli suite of algebraic objects like e.g. schemes, singularities or Lie algebras and provides a framework for this. The basic idea is to work with the action of the kernel of the Kodaira-Spencer map, on the base space of a versal family. The main results are the existence, in a general context, of a local moduli suite in the category of algebraic spaces, and the proof that, generically, this moduli suite is the quotient of a canonical filtration of the base space of the versal family by the action of the Kodaira-Spencer kernel. Applied to the special case of quasihomogenous hypersurfaces, these ideas provide the framework for the proof of the existence of a coarse moduli scheme for plane curve singularities with fixed semigroup and minimal Tjurina number . An example shows that for arbitrary the corresponding moduli space is not, in general, a scheme. The book addresses mathematicians working on problems of moduli, in algebraic or in complex analytic geometry. It assumes a working knowledge of deformation theory.

Keywords

Morphismus algebra automorphism deformation theory moduli space semigroup

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078937
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19235-0
  • Online ISBN 978-3-540-39153-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book