Morphisms of closed Riemann surfaces and Lefschetz trace formula
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- by Masaharu Tanabe PDF
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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.References
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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
- Received by editor(s): May 1, 2009
- Published electronically: December 1, 2009
- Communicated by: Franc Forstneric
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1295-1303
- MSC (2010): Primary 30F30; Secondary 58A14
- DOI: https://doi.org/10.1090/S0002-9939-09-10210-1
- MathSciNet review: 2578523