Equinormalizable theory for plane curve singularities with embedded points and the theory of equisingularity

Abstract

In this paper we give some criteria for a family of generically reduced plane curve singularities to be equinormalizable. The first criterion is based on the δ-invariant of a (non-reduced) curve singularity which is introduced by Brücker-Greuel ([BG]). The second criterion is based on the I-equisingularity of a k-parametric family (k ≥ 1) of generically reduced plane curve singularities, which is introduced by Nobile ([No]) for one-parametric families. The equivalence of some kinds of equisingularities of a family of generically reduced plane curve singularities is also studied.