Enriques Diagrams and Adjacency of Planar Curve Singularities

[摘要] We study adjacency of equisingularity types of planar complexcurve singularitiesin terms of their Enriques diagrams. The goal is, given two equisingularitytypes, to determine whether one of them is adjacent to the other. For linearadjacency a complete answer is obtained, whereas for arbitrary (analytic)adjacency a necessary condition and a sufficient condition areproved. We also obtain new examples of exceptional deformations, {em i.e.,} singular curves of type$mathcal{D}'$ that can be deformed to a curve of type $mathcal{D}$ without$mathcal{D}'$ being adjacent to $mathcal{D}$.

[学科分类] 数学（综合）