Mixed functions of strongly polar weighted homogeneous face type

Abstract

Let $f(\mathbf{z},\bar{\mathbf{z}})$ be a mixed polynomial with strongly non-degenerate face functions. We consider a canonical toric modification $\pi :X\to {\mathbb{C}}^n$ and a polar modification ${\pi }_{\mathbb{R}}:Y\to X$. We will show that the toric modification resolves topologically the singularity of $V$ and the zeta function of the Milnor fibration of $f$ is described by a formula of a Varchenko type.