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ISSN 1088-6826(e) ISSN 0002-9939(p)

Morphisms of closed Riemann surfaces and Lefschetz trace formula

Author(s): Masaharu Tanabe
Journal: Proc. Amer. Math. Soc. 138 (2010), 1295-1303.
MSC (2010): Primary 30F30; Secondary 58A14
Posted: 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 and J. 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: 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
Posted: December 1, 2009
Communicated by: Franc Forstneric
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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