Advanced Studies in Pure Mathematics

Mixed functions of strongly polar weighted homogeneous face type

Mutsuo Oka

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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

Singularities in Geometry and Topology 2011, V. Blanlœil and O. Saeki, eds. (Tokyo: Mathematical Society of Japan, 2015), 173-202

Received: 26 January 2012
Revised: 19 July 2012
First available in Project Euclid: 19 October 2018

Permanent link to this document euclid.aspm/1539916287

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14P05: Real algebraic sets [See also 12D15, 13J30] 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45]

Strongly polar weighted homogeneous Milnor fibration toric modification


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.

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