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Specialization to the tangent cone and Whitney equisingularity

Arturo Giles Flores (2013)

Bulletin de la Société Mathématique de France

Let ( X , 0 ) be a reduced, equidimensional germ of an 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 ϕ : 𝔛 to satisfy Whitney’s conditions along the parameter axis Y . This result is a first step in generalizing to higher dimensions Lê and Teissier’s result for hypersurfaces of 3 which establishes the Whitney equisingularity of X and its tangent cone under...

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