2000/10/13 by Vadim Kaloshin, V. A. Kaloshin, Kaloshin, Vadim
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.math/0010144
7 pages
arxiv created 2000/10/13 · openalex publication_date 2000/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A stratification of a singular set, e.g. an algebraic or analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together "regularly". A classical theorem of Whitney says that any complex analytic set has a stratification. This result was extended by Lojasiewicz to real (semi)analytic sets. In this paper we present a short geometric proof of existence of stratifications based on Thom's transversality theorem and Milnor's curve selection lemma and not relying on difficult results of Lojasiewicz.