Advertisement

Dynkin Graphs and Quadrilateral Singularities

  • Authors
  • Tohsuke¬†Urabe

Part of the Lecture Notes in Mathematics book series (LNM, volume 1548)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Tohsuke Urabe
    Pages 1-16
  3. Tohsuke Urabe
    Pages 98-184
  4. Tohsuke Urabe
    Pages 185-226
  5. Back Matter
    Pages 227-233

About this book

Introduction

The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs will attract attention of researches.

Keywords

Algebraic Curve Algebraic Geometry Deformation Dynkin Graph Graph Sim Singularity singular fiber

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0084369
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56877-3
  • Online ISBN 978-3-540-47769-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site