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The geometric genus of splice-quotient singularities
Author(s):
Tomohiro
Okuma
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6643-6659.
MSC (2000):
Primary 32S25;
Secondary 14B05, 14J17
Posted:
July 22, 2008
MathSciNet review:
2434304
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Additional information
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:
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
Posted:
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.
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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