Topological types of seven classes of isolated singularities with \(C^*\)-action
It is known [from \textit{P. Orlik} and \textit{P. Wagreich}, Ann. Math. (2) 93, 205--228 (1971; Zbl 0212.53702) and \textit{V. I. Arnol'd}, Russ. Math. Surv. 29, No. 2, 10--50 (1974); translation from Usp. Mat. Nauk 29, No. 2(176), 11--49 (1974; Zbl 0298.57022), two references, cited in the article] that if \(h: \mathbb C^ 3\to\mathbb C\) is a weighted homogeneous polynomial having an isolated singularity at the origin, then \(V=\{h=0\}\) can be deformed into a member of seven classes explicitly listed, while keeping the link \(K_ V\) differentiably constant. The purpose of this paper is to state and prove 28 statements \((28=C^ 1_ 7+C^ 2_ 7)\) which describe the members of these seven classes which have the same topological type (this means the existence of a homeomorphism between the pair of germs \((\mathbb C^ 3,V,0))\).
weighted homogeneous isolated singularities
scientific article; zbMATH DE number 168050