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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Morphisms of closed Riemann surfaces and Lefschetz trace formula


Author: Masaharu Tanabe
Journal: Proc. Amer. Math. Soc. 138 (2010), 1295-1303
MSC (2010): Primary 30F30; Secondary 58A14
Published electronically: December 1, 2009
MathSciNet review: 2578523
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Abstract: We study the number of coincidences of two distinct morphisms $ f_i :X\to Y (i=1,2)$ between closed Riemann surfaces of genera greater than zero. We give a necessary and sufficient condition for the existence of a coincidence in terms of the inner product defined on the free abelian group of homomorphisms between the Jacobian varieties J$ (X)$ and J$ (Y)$. We use the Hodge decomposition and the holomorphic Lefschetz number to study the number of coincidences in detail.


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Additional Information

Masaharu Tanabe
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo, Japan, 152-8551
Email: tanabe@math.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10210-1
PII: S 0002-9939(09)10210-1
Keywords: Riemann surfaces, Lefschetz trace formula, Hodge decomposition
Received by editor(s): May 1, 2009
Published electronically: December 1, 2009
Communicated by: Franc Forstneric
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.