Paper Info
Title
Constructibility of the set of polynomials with a fixed Bernstein-Sato polynonmial: an algorithmic approach
Abstract
Let nand d be positive integers, let k be a field and let P(n,d;k) be the space of the non-zero polynomials in n variables of degree at most d with coefficients in k. Let B(n,d) be the set of the Bernstein-Sato polynomials of all polynomials in P(n,d;k) as k varies over all fields of characteristic 0. G. Lyubeznik proved that B(n,d) is a finite set and asked if, for a fixed k, the set of the polynomials corresponding to each element of B(n,d) is a constructible subset of P(n,d;k). In this paper we give an affirmative answer to Lyubeznik's question by showing that the set in question is indeed constructible and definded over Q, i.e. its defining equations are the same for all fields k. Moreover, we construct an algorithm that for each pair (n,d) produces a complete list of the elements of B(n,d) and, for each element of this list, an explicit description of the constructible set of polynomials having this particular Bernstein-Sato polynomial. 2001 Academic Press.
Year
DOI
Venue
2001
10.1006/jsco.2001.0488
J. Symb. Comput.
Keywords
DocType
Volume
complete list,particular Bernstein-Sato polynomial,Bernstein-Sato polynomial,algorithmic approach,G. Lyubeznik,constructible subset,Academic Press,affirmative answer,finite set,fixed Bernstein-Sato polynonmial,fields k,fixed k
Journal
32
Issue
ISSN
Citations 
6
Journal of Symbolic Computation
5
PageRank 
References 
Authors
0.73
2
1
Name
Order
Citations
PageRank
Anton Leykin117318.99