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Topology types and multiplicites of isolated quasi-homogeneous surface singularities. (English) Zbl 0659.32013

Several mathematicians study the relationships among the topological type, the characteristic polynomial (i.e., the quasi-homogeneous type) and the fundamental group for the link, for two germs of 2-dimensional isolated quasi-homogeneous hypersurface singularities. And, we can see many results about that. In this paper, the author studies that two germs of 2-dimensional isolated quasi-homogeneous hypersurface singularities have the same topological type if and only if they have the same characteristic polynomial and the same fundamental group for their links.
Next Theorem solves the Zariski question completely in the case of quasi- homogeneous surface singularities in \({\mathbb{C}}^ 3\). Let (V,0) and (W,0) be two isolated quasi-homogeneous surface singularities in \({\mathbb{C}}^ 3\). If \(({\mathbb{C}}^ 3,V,0)\) is homeomorphic to \(({\mathbb{C}}^ 3,W,0)\) as a germ, the V and W have the same multiplicity at the origin.
Reviewer: S.Ohyanagi

MSC:

32B99 Local analytic geometry
32Sxx Complex singularities
14J17 Singularities of surfaces or higher-dimensional varieties
32S05 Local complex singularities
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