On Equisingularity of Families of Maps (ℂn, 0) → (ℂn+1, 0)
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A classical theorem of Briançon, Speder and Teissier states that a family of isolated hypersurface singularities is Whitney equisingular if, and only if, the μ*-sequence for a hypersurface is constant in the family. This paper shows that the constancy of relative polar multiplicities and the Euler characteristic of the Milnor fibres of certain families of non-isolated singularities is equivalent to the Whitney equisingularity of a family of corank 1 maps from n-space to n + 1-space. The number of invariants needed is 4n − 2, which greatly improves previous general estimates.
KeywordsWhitney stratification equisingularity
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