Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type (Q2059566)

Mixed analytic functions are new class of singularities. They are defined as complex valued real analytic functions by the formula \(f(z):=F(z,\bar{z}),\) where \(F(z,w)\) is a complex holomorphic function in two systems of variables \(z,w\) defined in a neighbourhood of \((0,0)\in \mathbb{C}^{n}\times \mathbb{C} ^{n}.\) It is denoted as \(f(z,\bar{z}).\) In the standard case where \(f(z)\) is a Newton non-degenerate (with respect to the Newton diagram \(\Gamma (f)\) of \( f\)) isolated singularity then toric modification associated with convenient regular subdivision of \(\Gamma (f)\) is a resolution of \(f^{-1}(0).\) The authors extend this result to mixed analytic case under some complicated assumptions and appropriate definitions of non-degeneracy. The first result of this type was given by \textit{M. Oka} [Adv. Stud. Pure Math. 66, 173--202 (2015; Zbl 1360.32028)]. The authors result is an extension of Oka result from strongly polar \textbf{ positive} mixed weighted homogeneous face type mixed analytic functions to strongly polar \textbf{non-negative} mixed weighted homogeneous face type ones (of course under additional assumpions).