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Popescu-Pampu, Patrick

Numerically Gorenstein surface singularities are homeomorphic to Gorenstein ones. (English) Zbl 1227.14010

Duke Math. J. 159, No. 3, 539-559 (2011).
A necessary condition for a normal surface singularity to be Gorenstein is that the cycle, obtained by solving the adjunction equations, has integral coefficients. The author proves that this condition (numerically Gorenstein), which depends only on the topological type, is sufficient for the existence of Gorenstein singularity of the same topological type. A resolution of the singularity is constructed by holomorphically plumbing total spaces of line bundles over curves, in such a way that the natural existing two forms extend. The constructed space has the special property that each irreducible component of the exceptional divisor has a neighbourhood isomorphic to a neighbourhood of the zero section of its normal bundle.
The result is extended to the \(\mathbb{Q}\)-Gorenstein case: any normal surface singularity is homeomorphic to a \(\mathbb{Q}\)-Gorenstein singularity.
Reviewer: Jan Stevens (Göteborg)

Cited in 1 Review
Cited in 5 Documents

MSC:

14B05 Singularities in algebraic geometry
32S25 Complex surface and hypersurface singularities
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants

Keywords:

Gorenstein singularity; numerical Gorenstein; plumbing
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\textit{P. Popescu-Pampu}, Duke Math. J. 159, No. 3, 539--559 (2011; Zbl 1227.14010)
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References:

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