Lipschitz stratification of complex hypersurfaces in codimension 2

  • Adam Parusiński

    Université Côte d’Azur, Nice, France
  • Laurenţiu Păunescu

    University of Sydney, Australia
Lipschitz stratification of complex hypersurfaces in codimension 2 cover
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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 the Zariski equisingular families of surface, not necessarily isolated, singularities in . 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, with trivializations obtained by integrating Lipschitz vector fields.

Cite this article

Adam Parusiński, Laurenţiu Păunescu, Lipschitz stratification of complex hypersurfaces in codimension 2. J. Eur. Math. Soc. 25 (2023), no. 5, pp. 1743–1781

DOI 10.4171/JEMS/1224