A Whitney stratification and equisingular family of quasi-ordinary singularities

Ban, Chunsheng

doi:10.1090/S0002-9939-1993-1107918-1

A Whitney stratification and equisingular family of quasi-ordinary singularities
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by Chunsheng Ban PDF

Proc. Amer. Math. Soc. 117 (1993), 305-311 Request permission

Abstract:

Let $(V,0) \subset ({{\mathbf {C}}^{d + 1}},0)$ be a quasi-ordinary singularity and $\pi :(V,0) \to ({{\mathbf {C}}^d},0)$ a quasi-ordinary projection. ${{\mathbf {C}}^d}$ has a natural Whitney stratification given by the multiplicities of the discriminant locus of $\pi$. It is proved that the pullback of this stratification gives a Whitney stratification of $(V,0)$. Then using this result, an equisingular family of quasi-ordinary singularities is studied.

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