Specialization to the tangent cone and Whitney Equisingularity
Algebraic Geometry
2011-06-08 v1
Abstract
Let (X,0) be a reduced, equidimensional germ of analytic singularity with reduced tangent cone (C_{X,0},0). We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part \X^0 of the specialization to the tangent cone \phi: \X \to \C to satisfy Whitney's conditions along the parameter axis Y. This result is a first step in generalizing to higher dimensions L\^e and Teissier's result for hypersurfaces of \C^3 which establishes the Whitney equisingularity of X and its tangent cone under this conditions.
Keywords
Cite
@article{arxiv.1106.1191,
title = {Specialization to the tangent cone and Whitney Equisingularity},
author = {Arturo Giles Flores},
journal= {arXiv preprint arXiv:1106.1191},
year = {2011}
}