The principle describing possible combinations of singularities in deformations of a fixed singularity

Abstract

This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed singularity? We consider this problem for hypersurface singularities on complex analytic spaces of dimension 2. For all singularities in the beginning par t of Arnold's classification list, the answer to this problem is given by a unique principle described by Dynkin graphs. This article contains several figures. I will send the hard copy containin g figures by mail with envelope and stamps under request.