2003/07/11 by Rouchdi Bahloul, Bahloul, Rouchdi
Mathematics · #13N10 #14R99 #16S32 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13N10 #msc:14R99 #msc:16S32
paper · pdf · doi:10.48550/arxiv.math/0307168
6 pages, no figures
arxiv created 2003/07/11 · openalex publication_date 2003/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given p polynomials with coefficients in a commutative unitary integral ring C containing ℚ, we define the notion of a generic Bernstein-Sato polynomial on an irreducible affine scheme V ⊂ Spec(C). We prove the existence of such a non zero rational polynomial which covers and generalizes previous existing results by H. Biosca. When C is the ring of an algebraic or analytic space, we deduce a stratification of the space of the parameters such that on each stratum, there is a non zero rational polynomial which is a Bernstein-Sato polynomial for any point of the stratum. This generalizes a result of A. Leykin obtained in the case p=1.