Specialization of Segre classes of singular algebraic varieties.
Let be a reduced, equidimensional germ of an analytic singularity with reduced tangent cone . We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part of the specialization to the tangent cone to satisfy Whitney’s conditions along the parameter axis . This result is a first step in generalizing to higher dimensions Lê and Teissier’s result for hypersurfaces of which establishes the Whitney equisingularity of and its tangent cone under...