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EQUINORMALIZABLE THEORY FOR PLANE CURVE SINGULARITIES WITH EMBEDDED POINTS AND THE THEORY OF EQUISINGULARITY

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Gravitational singularity, Plane curve, Mathematics, Equivalence (formal languages), Singularity, Pure mathematics, Singularity theory, Invariant (physics)

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