Oka, Mutsuo Topology of polar weighted homogeneous hypersurfaces. (English) Zbl 1149.14031 Kodai Math. J. 31, No. 2, 163-182 (2008). Polar weighted homogeneous polynomials are special polynomials of real variables \(x_j\), \(y_j\) with \(z_j =x_j + i y_j\), \(0 \leq j \leq n \) wich enjoy a polar action. Their behaviour looks like that complex weighted homogeneous polynomials. A polynomial \(f\) as above defines a global filtration \(f: \mathbb{C}^n - f^{-1} (0) \rightarrow \mathbb{C}^*\). The author studies the topology of the hypersurface \(F=f^{-1}(1)\) which is a fiber of the above filtration. \(F\) has a canonical stratification with strata \(F^{*I}\), \(I \subset \{1, 2, \ldots, n \}\) and the main result describes the topology of \(F^{*I}\) for a simplicial polar weighted polynomial. Reviewer: Carlos Galindo (Castellon) Cited in 2 ReviewsCited in 34 Documents MSC: 14J17 Singularities of surfaces or higher-dimensional varieties 32S25 Complex surface and hypersurface singularities Keywords:polar weighted homogeneous polynomials; polar action PDFBibTeX XMLCite \textit{M. Oka}, Kodai Math. J. 31, No. 2, 163--182 (2008; Zbl 1149.14031) Full Text: DOI arXiv