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A note on resolution of rational and hypersurface singularities

D. A. Stepanov
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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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D. A. Stepanov. 2009-04-22. A note on resolution of rational and hypersurface singularities. https://arxiv.org/abs/math/0602080

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