Dynkin Graphs, Gabriélov Graphs and Triangle Singularities

1996/11/10 by Tohsuke Urabe, Urabe, Tohsuke
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9611011

10 pages with six postscript figures. AMSLaTeX v 1.2.figures. Adobe PDF version is available also at my private homepage, http://urabe-lab.math.metro-u.ac.jp/PreprintListE.html

arxiv created 1996/11/17 · arxiv updated 2009/11/30

Abstract

Fourteen kinds of triangle singularities with modality one in Arnold's classification list are discussed. We consider which kinds of combinations of rational double points can appear on small deformation fibers of the singularities. We show that possible combinations of rational double points can be described by a unique principle from the view point of Dynkin graphs.

Related

• Dynkin Graphs and Triangle Singularities
• The Dynkin diagrams of rational double points
• The principle describing possible combinations of singularities in deformations of a fixed singularity
• Singularity categories of rational double points in arbitrary characteristic
• A geometric definition of Gabrielov numbers