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 4n − 2, which greatly improves previous general estimates.
This work was initially carried out when the author visited ICMC at USP in São Carlos, Brazil. He is grateful to Maria Ruas for the hospitality during his stay and expresses his thanks to EPSRC for funding (Grant reference GR/S48639/01). Thanks are also due to the referee who made a number of useful comments.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Houston, K. (2006). On Equisingularity of Families of Maps (ℂn, 0) → (ℂn+1, 0). In: Brasselet, JP., Ruas, M.A.S. (eds) Real and Complex Singularities. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7776-2_14
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DOI: https://doi.org/10.1007/978-3-7643-7776-2_14
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