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  • © 1988

Local Moduli and Singularities

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-V
  2. Introduction

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 1-7
  3. The prorepresenting substratum of the formal moduli

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 8-14
  4. Automorphisms of the formal moduli

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 15-31
  5. The kodaira-spencer map and its kernel

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 32-60
  6. Applications to isolated hypersurface singularities

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 61-71
  7. Plane curve singularities with k*-action

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 72-87
  8. The generic component of the local moduli suite

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 88-104
  9. The moduli suite of x 1 5 +x 2 11

    • Olav Arnfinn Laudal, Gerhard Pfister
    Pages 105-111
  10. Back Matter

    Pages 112-117

About this book

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

  • Book Title: Local Moduli and Singularities

  • Authors: Olav Arnfinn Laudal, Gerhard Pfister

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078937

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19235-0Published: 25 May 1988

  • eBook ISBN: 978-3-540-39153-1Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 120

  • Topics: Algebraic Geometry, Topological Groups and Lie Groups

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions