Equisingularity of families of hypersurfaces and applications to mappings
arXiv:0803.1756
Abstract
In the study of equisingularity of isolated singularities we have the classical theorem of Briancon, Speder and Teissier which states that a family of isolated hypersurface singularities is Whitney equisingular if and only if the mu^*-sequence for a hypersurface is constant in the family. In this paper we generalize to non-isolated hypersurface singularities. By assuming non-contractibility of strata of a Whitney stratification of the non-isolated singularities outside the origin we show that Whitney equisingularity of a family is equivalent to constancy of a certain selection of invariants from two distinct generalizations of the mu^*-sequence. Applications of this theorem to equisingularity of more general mappings are given.
The new version clarifies part of Lemma 5.2 and contains a new proposition that justifies a step in Lemma 5.3 (now 5.4) that no-one seemed to believe