D. A. Stepanov
Published 2006-02-05, updated 2009-04-22Version 3
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.
Comments: 10 pages, the structure of the paper has been slightly revised and a mistake in the proof of degeneration of spectral sequence in Lemma 2.3 (Lemma 2.4 of the published version of the paper) has been corrected
Journal: Proc. Amer. Math. Soc. 136 (2008), 2647-2654
Combinatorial structure of exceptional sets in resolutions of singularities
On a resolution of singularities with two strata
A Game for the Resolution of Singularities
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