Mathematics – Algebraic Geometry
Scientific paper
2010-11-30
Mathematics
Algebraic Geometry
16 pages, replaced Example 2.1 and Example 3.1, added Example 4.1 and Example 4.2, to appear in Hokkaido Mathematical Journal
Scientific paper
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 $\delta$-invariant of a (non-reduced) curve singularity which is introduced by Br\"{u}cker-Greuel (\cite{BG}). The second criterion is based on the I-equisingularity of a $k$-parametric family ($k\geq 1$) of generically reduced plane curve singularities, which is introduced by Nobile (\cite{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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