Abstract
Let $f(\mathbf z,\bar{\mathbf z})$ 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 $f(\mathbf z,\bar{\mathbf z})$ under the Assumption(*) (Theorem 32). This result is an extension of the first part of Theorem 11 ([4]) by M. Oka, which studies strongly polar positive cases, to strongly polar non-negative cases. We also consider some typical examples (§9).
Acknowledgment
The authors would like to thank the referee for careful readings and many good advices, Professor Mutsuo Oka (Tokyo University of Science) for his kind and good advices, and Professor Toru Ohmoto (Hokkaido University) for introducing them studies of mixed functions.
Citation
Sachiko Saito. Kosei Takashimizu. "Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type." Kodai Math. J. 44 (3) 457 - 491, October 2021. https://doi.org/10.2996/kmj/kmj44304
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