Equisingularity of map germs from a surface to the plane

2015/07/06 by Nuño-Ballesteros, J. J., Oréfice-Okamoto, B., Tomazella, J. N.
#32S15 #58K40 #58K60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.01483

Abstract

Let (X,0) be an ICIS of dimension 2 and let f:(X,0)→ (\C²,0) be a map germ with an isolated instability. We look at the invariants that appear when X_s is a smoothing of (X,0) and f_s:X_s→ B_ε is a stabilization of f. We find relations between these invariants and also give necessary and sufficient conditions for a 1-parameter family to be Whitney equisingular. As an application, we show that a family (X_t,0) is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant on t.

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