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A note on resolution of rational and hypersurface singularities


Author: D. A. Stepanov
Journal: Proc. Amer. Math. Soc. 136 (2008), 2647-2654
MSC (2000): Primary 14B05; Secondary 32S50
DOI: https://doi.org/10.1090/S0002-9939-08-09289-7
Published electronically: April 11, 2008
Erratum: Proc. Amer. Math. Soc. 138 (2010), 3019-3020
MathSciNet review: 2399025
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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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Additional Information

D. A. Stepanov
Affiliation: Department of Mathematical Modeling, Bauman Moscow State Technical University, Moscow 105005, Russia
Email: dstepanov@bmstu.ru

DOI: https://doi.org/10.1090/S0002-9939-08-09289-7
Keywords: Rational singularity, hypersurface singularity, resolution of singularities, the dual complex associated to a resolution
Received by editor(s): March 20, 2006
Received by editor(s) in revised form: July 2, 2006, and November 16, 2006
Published electronically: April 11, 2008
Additional Notes: This research was supported by RFBR, grant no. 05-01-00353, CRDF, grant no. RUM1-2692-MO-05, and the Program for the Development of Scientific Potential of the High School, no. 2.1.1.2381.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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