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arXiv · 1906.03086

Bernstein-Sato polynomials for general ideals vs. principal ideals

Mircea Mustata
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Abstract

We show that given an ideal I generated by regular functions f_1,...,f_r on the smooth complex variety X, the Bernstein-Sato polynomial of I is equal to the reduced Bernstein-Sato polynomial of the function g=\sum_{i=1}^rf_iy_i on the product of X with an r-dimensional affine space. By combining this with results from [BMS], we relate invariants and properties of I 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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Mircea Mustata. 2019-06-12. Bernstein-Sato polynomials for general ideals vs. principal ideals. https://arxiv.org/abs/1906.03086

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