Monodromy conjecture for semi-quasihomogeneous hypersurfaces

Abstract

We give a proof the monodromy conjecture relating the poles of motivic zeta functions with roots of b-functions for isolated quasihomogeneous hypersurfaces, and more generally for semi-quasihomogeneous hypersurfaces. We also give a strange generalization allowing a twist by certain differential forms.

A mistake in Section 3 was pointed out by M. Saito. An erratum is added as the last page. The results in the Introduction are not affected