A note on resolution of rational and hypersurface singularities

Stepanov, D.

doi:10.1090/S0002-9939-08-09289-7

A note on resolution of rational and hypersurface singularities
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Proc. Amer. Math. Soc. 136 (2008), 2647-2654 Request permission

Erratum: Proc. Amer. Math. Soc. 138 (2010), 3019-3020.

Abstract:

It is well known that the exceptional set in a resolution of a rational surface singularity is a tree of rational curves. We generalize the combinatoric part of this statement to higher dimensions and show that the highest cohomologies of the dual complex associated to a resolution of an isolated rational singularity vanish. We also prove that the dual complex associated to a resolution of an isolated hypersurface singularity is simply connected. As a consequence, we show that the dual complex associated to a resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy type of a point.

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