Bernstein-Sato polynomials for general ideals vs. principal ideals

Mustaţă, Mircea

doi:10.1090/proc/14996

Bernstein-Sato polynomials for general ideals vs. principal ideals
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Proc. Amer. Math. Soc. 150 (2022), 3655-3662 Request permission

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.

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