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.