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

Abstract

Let f(z, z̄) be a convenient Newton non-degenerate mixed polynomial with strongly polar nonnegative mixed weighted homogeneous face functions. We consider a convenient regular simplicial cone subdivision Σ∗ which is admissible for f and take the toric modification π̂ : X → C associated with Σ∗. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by f(z, z̄) 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).