Bernstein-Sato polynomials for general ideals vs. principal ideals
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- by Mircea Mustaţă
- Proc. Amer. Math. Soc. 150 (2022), 3655-3662
- DOI: https://doi.org/10.1090/proc/14996
- Published electronically: June 3, 2022
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Abstract:
We show that given an ideal $\mathfrak {a}$ generated by regular functions $f_1,\ldots ,f_r$ on $X$, the Bernstein-Sato polynomial of $\mathfrak {a}$ is equal to the reduced Bernstein-Sato polynomial of the function $g=\sum _{i=1}^rf_iy_i$ on $X\times \mathbf {A}^r$. By combining this with results from Budur, Mustaţă, and Saito [Compos. Math. 142 (2006), pp. 779–797], we relate invariants and properties of $\mathfrak {a}$ to those of $g$. We also use the result on Bernstein-Sato polynomials to show that the Strong Monodromy Conjecture for Igusa zeta functions of principal ideals implies a similar statement for arbitrary ideals.References
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Bibliographic Information
- Mircea Mustaţă
- Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
- Email: mmustata@umich.edu
- Received by editor(s): June 16, 2019
- Received by editor(s) in revised form: December 16, 2019
- Published electronically: June 3, 2022
- Additional Notes: The author was partially supported by NSF grant DMS-1701622 and a Simons Fellowship.
- Communicated by: Rachel Pries
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3655-3662
- MSC (2020): Primary 14F10; Secondary 14E18, 14F18
- DOI: https://doi.org/10.1090/proc/14996
- MathSciNet review: 4446219