Algebro-geometric equisingularity of Zariski

2020/10/18 by Adam Parusiński, Parusiński, Adam · 1 citation
Mathematics · Physics and Astronomy · #14B05 #32B10 #32Sxx #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2010.08927

openalex publication_date 2020/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Ploski Approximation Theorem

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