Equisingularity of families of hypersurfaces and applications to mappings

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dc.creatorHouston, Kevin
dc.date2008-03-12
dc.date2008-07-02
dc.date.accessioned2026-07-07T09:47:48Z
dc.date.available2026-07-07T09:47:48Z
dc.descriptionIn 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.
dc.descriptionThe 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
dc.identifierhttps://arxiv.org/abs/0803.1756
dc.identifierhttp://arxiv.org/abs/0803.1756
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163976
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.subject32S15; 32S30; 32S60
dc.titleEquisingularity of families of hypersurfaces and applications to mappings
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