## Advanced Studies in Pure Mathematics

### Mixed functions of strongly polar weighted homogeneous face type

Mutsuo Oka

#### 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.

#### Article information

Dates
Revised: 19 July 2012
First available in Project Euclid: 19 October 2018

https://projecteuclid.org/ euclid.aspm/1539916287

Digital Object Identifier
doi:10.2969/aspm/06610173

Mathematical Reviews number (MathSciNet)
MR3382050

Zentralblatt MATH identifier
1360.32028

#### Citation

Oka, Mutsuo. Mixed functions of strongly polar weighted homogeneous face type. Singularities in Geometry and Topology 2011, 173--202, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06610173. https://projecteuclid.org/euclid.aspm/1539916287