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Algebro-Geometric Equisingularity of Zariski

In: Handbook of Geometry and Topology of Singularities II

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  • Adam Parusiński

    (Université Côte d’Azur, CNRS, LJAD, UMR 7351)

Abstract

This is a survey on Zariski equisingularity. We recall its definition, main properties, and a variety of applications in Algebraic Geometry and Singularity Theory. In the first part of this survey, we consider Zariski equisingular families of complex analytic or algebraic hypersurfaces. We also discuss how to construct Zariski equisingular deformations. In the second part, we present Zariski equisingularity of hypersurfaces along a nonsingular subvariety and its relation to other equisingularity conditions. We also discuss the canonical stratification of such hypersurfaces given by the dimensionality type.

Suggested Citation

  • Adam Parusiński, 2021. "Algebro-Geometric Equisingularity of Zariski," Springer Books, in: José Luis Cisneros-Molina & Dũng Tráng Lê & José Seade (ed.), Handbook of Geometry and Topology of Singularities II, chapter 0, pages 177-222, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-78024-1_4
    DOI: 10.1007/978-3-030-78024-1_4
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