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

Abstract

Let $f(z,\bar{z})$ 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 ${\Sigma }^{\ast }$ which is admissible for $f$ and take the toric modification $\hat{\pi }:X\to {\mathbb{C}}^n$ associated with ${\Sigma }^{\ast }$. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by $f(z,\bar{z})$ 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 (§9).

24 pages

Cited by in corpus (1)

• A note on Newton non-degeneracy of mixed weighted homogeneous polynomials