Equisingularity of families of map germs from the plane to 3-space

2023/09/04 by da Silva, Otoniel Nogueira
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.01846

Abstract

In this work, we consider a finitely determined map germ f from (ℂ²,0) to (ℂ³,0). We characterize the Whitney equisingularity of an unfolding F=(f_t,t) of f through the constancy of a single invariant in the source. Namely, the Milnor number of the curve W_t(f)=D(f_t)∪ f_t^-1(γ), where D(f) denotes the double point curve of f_t. This gives an answer to a question by Ruas in 1994.

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