On Igusa zeta functions of monomial ideals

Abstract

We show that the real parts of the poles of the Igusa zeta function of a monomial ideal can be computed from the torus-invariant divisors on the normalized blowing-up along the ideal. Moreover, we show that every such number is a root of the Bernstein-Sato polynomial associated to the monomial ideal.

10 pages; to appear in Proc. Amer. Math. Soc