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arXiv · 1909.00296

Lipschitz Stratification of Complex Hypersurfaces in Codimension 2

Adam Parusinski·Laurentiu Paunescu
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Abstract

We show that the Zariski canonical stratification of complex hypersurfaces is locally bi-Lipschitz trivial along the strata of codimension two. More precisely, we study Zariski equisingular families of surface, not necessarily isolated, singularities in $\mathbb{C}^3$. We show that a natural stratification of such a family given by the singular set and the generic family of polar curves provides a Lipschitz stratification in the sense of Mostowski. In particular, such families are bi-Lipschitz trivial by trivializations obtained by integrating Lipschitz vector fields.

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Adam Parusinski, Laurentiu Paunescu. 2019-09-01. Lipschitz Stratification of Complex Hypersurfaces in Codimension 2. https://arxiv.org/abs/1909.00296

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