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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Bernstein-Sato polynomials


Author: Gennady Lyubeznik
Journal: Proc. Amer. Math. Soc. 125 (1997), 1941-1944
MSC (1991): Primary 13N10, 16S32
MathSciNet review: 1372038
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Abstract: We show that for fixed $n$ and $d$ the set of Bernstein-Sato polynomials of all the polynomials in at most $n$ variables of degrees at most $d$ is finite. As a corollary, we show that there exists an integer $t$ depending only on $n$ and $d$ such that $f^{-t}$ generates $R_f$ as a module over the ring of the $k$-linear differential operators of $R$, where $k$ is an arbitrary field of characteristic 0, $R$ is the ring of polynomials in $n$ variables over $k$ and $f\in R$ is an arbitrary non-zero polynomial of degree at most $d$.


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Additional Information

Gennady Lyubeznik
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: gennady@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03774-X
PII: S 0002-9939(97)03774-X
Received by editor(s): December 4, 1995
Received by editor(s) in revised form: January 22, 1996
Additional Notes: The author was partially supported by the NSF
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society