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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The geometric genus of splice-quotient singularities


Author: Tomohiro Okuma
Journal: Trans. Amer. Math. Soc. 360 (2008), 6643-6659
MSC (2000): Primary 32S25; Secondary 14B05, 14J17
Published electronically: July 22, 2008
MathSciNet review: 2434304
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Abstract: We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.


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Additional Information

Tomohiro Okuma
Affiliation: Department of Education, Yamagata University, Yamagata 990-8560, Japan
Email: okuma@e.yamagata-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04559-5
PII: S 0002-9947(08)04559-5
Keywords: Surface singularity, geometric genus, rational homology sphere, splice type singularity, universal abelian cover
Received by editor(s): October 18, 2006
Received by editor(s) in revised form: March 13, 2007
Published electronically: July 22, 2008
Additional Notes: This work was partly supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.