Real and Complex Singularities pp 201-208 | Cite as

# On Equisingularity of Families of Maps (ℂ^{n}, 0) → (ℂ^{n+1}, 0)

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## Abstract

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 4*n* − 2, which greatly improves previous general estimates.

## Keywords

Whitney stratification equisingularity## Preview

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© Birkhäuser Verlag Basel/Switzerland 2006