A multiplicity formula for the Milnor number of smoothable curves

Author:

Andrei Benguş-Lasnier, Terence Gaffney, Antoni Rangachev

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC), Complex Variables (math.CV)

journal:

date:

2023-10-24 16:00:00

Abstract

We derive a multiplicity formula for the Milnor number of a reduced smoothable curve singularity generalizing a well-known formula due to L\^e, Greuel and Teissier for complete intersection curves. We obtain a multiplicity characterization of Whitney equisingularity for families of locally smoothable curves.

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