The strong monodromy conjecture for monomial ideals on toric varieties

Abstract

We compute Denef and Loeser’s motivic zeta function associated to a monomial ideal on an affine toric variety, generalizing a result of Howald, Mustaţă, and Yuen. We also investigate the relation between the poles of the motivic zeta function and the roots of their corresponding Bernstein–Sato polynomial defined by the first author and Matusevich.