2015/02/28 by Adam Parusiński, Parusiński, Adam, Laurentiu Paunescu +2 · 1 citation
Computer Science · Mathematics · #14P25 #32S15 #32S60 #32Sxx #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CV #msc:14P25 #msc:32S15 #msc:32S60 #msc:32Sxx
paper · pdf · doi:10.48550/arxiv.1503.00130
45 pages, new constructive proof ot the main result
openalex publication_date 2015/02/28 · arxiv created 2017/01/24 · arxiv updated 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we show Whitney's fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivialization arc-wise analytic and we show that it can be constructed under the classical Zariski algebro-geometric equisingularity assumptions. Using a slightly stronger version of Zariski equisingularity, we show the existence of Whitney's stratified fibration, satisfying the conditions (b) of Whitney and (w) of Verdier. Our construction is based on Puiseux with parameter theorem and a generalization of Whitney interpolation. For algebraic sets our construction gives a global stratification. We also give several applications of arc-wise analytic trivialization, mainly to the stratification theory and the equisingularity of analytic set and function germs. In the real algebraic case, for an algebraic family of projective varieties, we show that Zariski equisingularity implies local triviality of the weight filtration.