Topology of polar weighted homogeneous hypersurfaces. (English) Zbl 1149.14031
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)
MSC:
14J17 | Singularities of surfaces or higher-dimensional varieties |
32S25 | Complex surface and hypersurface singularities |