On Bernstein-Sato polynomials
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- by Gennady Lyubeznik PDF
- Proc. Amer. Math. Soc. 125 (1997), 1941-1944 Request permission
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 $d$.References
- J.-E. Björk, Rings of differential operators, North-Holland Mathematical Library, vol. 21, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 549189
- André Galligo, Some algorithmic questions on ideals of differential operators, EUROCAL ’85, Vol. 2 (Linz, 1985) Lecture Notes in Comput. Sci., vol. 204, Springer, Berlin, 1985, pp. 413–421. MR 826576, DOI 10.1007/3-540-15984-3_{3}01
Additional Information
- Gennady Lyubeznik
- Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 117320
- Email: gennady@math.umn.edu
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1941-1944
- MSC (1991): Primary 13N10, 16S32
- DOI: https://doi.org/10.1090/S0002-9939-97-03774-X
- MathSciNet review: 1372038