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A note on resolution of rational and hypersurface singularities
Author(s):
D.
A.
Stepanov
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2647-2654.
MSC (2000):
Primary 14B05;
Secondary 32S50
Posted:
April 11, 2008
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Additional information
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:
10.1090/S0002-9939-08-09289-7
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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