Whitney equisingularity of families of surfaces in ℂ³

2016/08/30 by Ruas, M. A. S., Silva, O. N. · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.08290

Abstract

In this work, we study families of singular surfaces in ℂ³ parametrized by A-finitely determined map germs. We consider the topological triviality and Whitney equisingularity of an unfolding F of a finitely determined map germ f:(ℂ²,0)→(ℂ³,0). We investigate the following conjecture: topological triviality implies Whitney equisingularity of the unfolding F? We provide a complete answer to this conjecture, given counterexamples showing how the conjecture can be false.

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• Transverse slices, Ruas' conjecture, and Zariski's multiplicity conjecture for quasihomogeneous surfaces

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• Transverse slices, Ruas' conjecture, and Zariski's multiplicity conjecture for quasihomogeneous surfaces
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