Hokkaido Mathematical Journal

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

Hokkaido Mathematical Journal, 41 (2012) pp.317-334

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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.

MSC(Primary)14B05
MSC(Secondary)14B07, 14B12, 14H20, 14H50
Uncontrolled KeywordsLocal deformations, equinormalizable, equisingularity, δ-invariant, plane curve singularities