Whitney equisingularity of families of surfaces in ${\mathbb{C}}^3$

Abstract

In this work, we study families of singular surfaces in ${\mathbb{C}}^3$ parametrized by $\mathcal{A}$-finitely determined map germs. We consider the topological triviality and Whitney equisingularity of an unfolding $F$ of a finitely determined map germ $f:({\mathbb{C}}^2,0)\to ({\mathbb{C}}^3,0)$. 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.

15 pages, 2 figures. Changes in version 2: the proof of Corollary 5.13 of version 1 was not corrected. In version 2, we present counterexamples for the result stated in version 1

References in corpus (1)

• Topological Triviality of Families of Singular Surfaces