Estimates for zero loci of Bernstein-Sato ideals
type: Item
instance of: scholarly article
title: Estimates for zero loci of Bernstein-Sato ideals
author: Nero Budur
author: Robin van der Veer
author: Alexander Van Werde
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2024-10-15T00:00:00Z
review text: Let \(F=(f_1,\cdots, f_r)\) be a family of polynomials in \(n\) variables with complex coefficients, with \(r>0\). To each \(a=(a_1,\cdots, a_r)\in\mathbb{N}^r\) such that \(f_1^{a_1}\cdots f_r^{a_r}\) admits zeros in \(\mathbb{C}^n\) one associates the Bernstein-Sato ideal \(B^a_F\) of \(\mathbb{C}[s_1,\cdots, s_r]\). The purpose of this paper is twofold:\N\NIn Theorem 1.2 the authors prove a refinement of the already known characterization of the 1-codimensional irreducible components of the zero locus of \(B^a_F\) (\(Z(B_F^a)\)) by means of log resolutions. Such a refinement implies upper bounds for \(Z(B_F^a)\).\N\NIn the second part (Section 4, with main result Theorem 1.4), using the language of polytopes, the authors obtain lower bounds for the same zero locus.\N\NThese results have an analytic version by considering germs of analytic morphisms.
reviewed by: Teresa Monteiro Fernandes
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 32S45
zbMATH DE Number: 7926547
zbMATH Keywords: Bernstein-Sato ideal
zbMATH Keywords: log resolution
MaRDI profile type: Publication
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DOI: 10.4171/PRIMS/60-3-7
description: scientific article; zbMATH DE number 7926547