The Intersection Structure of Bernstein-Sato Ideals

Abstract: By using logarithmic $\mathcal D$-modules and Gr\"obner bases, we prove that Bernstein-Sato ideals satisfy some symmetric intersection property, answering a question posed by Budur. As an application, we obtain a formula for the Bernstein-Sato polynomials of $f<sup>n$, the integer powers of a multi-variable polynomial $f$.