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Consider a normal complex analytic surface singularity. It is calledGorenstein if the canonical line bundle is holomorphically trivial in somepunctured neighborhood of the singular point and is called numericallyGorenstein if this line bundle is topologically trivial. The second notiondepends only on the topological type of the singularity. Laufer proved in 1977that, given a numerically Gorenstein topological type of singularity, everyanalytical realization of it is Gorenstein if and only if one has either aKleinian or a minimally elliptic topological type. The question to know if anynumerically Gorenstein topology was realizable by some Gorenstein singularitywas left open. We prove that this is indeed the case. Our method is to plumbholomorphically meromorphic 2-forms obtained by adequate pull-backs of thenatural holomorphic symplectic forms on the total spaces of the canonical linebundles of complex curves. More generally, we show that any normal surfacesingularity is homeomorphic to a Q-Gorenstein singularity whose index is equalto the smallest common denominator of the coefficients of the canonical cycleof the starting singularity.

Numerically Gorenstein surface singularities are homeomorphic to Gorenstein ones