A note on resolution of rational and hypersurface singularities
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.
Cite
@article{arxiv.math/0602080,
title = {A note on resolution of rational and hypersurface singularities},
author = {D. A. Stepanov},
journal= {arXiv preprint arXiv:math/0602080},
year = {2009}
}
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