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arXiv · 2101.09631

Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type

Sachiko Saito·Kosei Takashimizu
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Abstract

Let $f(\mathbb{z},\bar{\mathbb{z}})$ be a convenient Newton non-degenerate mixed polynomial with strongly polar non-negative mixed weighted homogeneous face functions. We consider a convenient regular simplicial cone subdivision $\Sigma^*$ which is admissible for $f$ and take the toric modification $\hat{\pi} : X \to \mathbb{C}^n$ associated with $\Sigma^*$. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by $f(\mathbb{z},\bar{\mathbb{z}})$ under the Assumption (*) (Theorem 32). This result is an extension of the first part of Theorem 11 ([4]) by Mutsuo Oka. We also consider some typical examples (\S 9).

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Sachiko Saito, Kosei Takashimizu. 2021-01-24. Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type. https://doi.org/10.2996/kmj%2Fkmj44304

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