Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 941-946

A MARTENS-TYPE THEOREM IN THE CONTEXT OF COHOMOLOGY OF RIEMANN SURFACES

Masaharu Tanabe

Tokyo Institute of Technology, Department of Mathematics
Ohokayama, Meguro, Tokyo, 152-8551, Japan; tanabe.m.ac 'at' m.titech.ac.jp

Abstract. A holomorphic map between closed Riemann surfaces is completely determined by the induced homomorphism of the first homology groups with integer coefficients. This is a consequence of Martens' theorem proven in [6]. In this paper, we study holomorphic maps of closed Riemann surfaces in the context of cohomology and extend Martens' theorem.

2010 Mathematics Subject Classification: Primary 14F40, 14H40, 30F30.

Key words: Riemann surfaces, cohomology, Jacobian varieties.

Reference to this article: M. Tanabe: A Martens-type theorem in the context of cohomology of Riemann surfaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 941-946.

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doi:10.5186/aasfm.2014.3938