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Classification of weighted dual graphs with only complete intersection singularities structures. (English) Zbl 1171.32016

Authors’ abstract: Let \(p\) be normal singularity of the \(2\)-dimensional Stein space \(V.\) Let \(\pi: M \to V\) be a minimal good resolution of \(V,\) such that the irreducible components \(A_{i}\) of \(A=\pi^{-1}(p)\) are nonsingular and have only normal crossings. Associated to \(A\) is weighted dual graph \(\Gamma\) which, along with the genera of the \(A_{i},\) fully describes the topology and differentiable structure of \(A\) and the topological and differentiable nature of the embedding of \(A\) in \(M.\) In this paper we give the complete classification of weighted dual graphs which have only complete intersection singularities but no hypersurface singularities associated to them. We also give the complete classification of weighted dual graphs which have only complete intersection singularities associated to them.

MSC:

32S25 Complex surface and hypersurface singularities
58K65 Topological invariants on manifolds
14B05 Singularities in algebraic geometry
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