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

 

Real forms of a Riemann surface of even genus


Authors: G. Gromadzki and M. Izquierdo
Journal: Proc. Amer. Math. Soc. 126 (1998), 3475-3479
MSC (1991): Primary 20F10, 30F10; Secondary 30F35, 51M10, 14H99
MathSciNet review: 1485478
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Abstract: Natanzon proved that a Riemann surface $X$ of genus $g \ge 2$ has at most $2(\sqrt g+1)$ conjugacy classes of symmetries, and this bound is attained for infinitely many genera $g$. The aim of this note is to prove that a Riemann surface of even genus $g$ has at most four conjugacy classes of symmetries and this bound is attained for an arbitrary even $g$ as well. An equivalent formulation in terms of algebraic curves is that a complex curve of an even genus $g$ has at most four real forms which are not birationally equivalent.


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Additional Information

G. Gromadzki
Affiliation: Institute of Mathematics University of Gdańsk, ul. Wita Stowsza 57, 80-952 Gdańsk, Poland

M. Izquierdo
Affiliation: Department of Mathematics, Mälardalen University, 721 23 Västerås, Sweden
Email: mio@mdh.se

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04735-2
PII: S 0002-9939(98)04735-2
Received by editor(s): April 14, 1997
Additional Notes: The second author was partially supported by The Swedish Natural Science Research Council (NFR)
Communicated by: Linda Keen
Article copyright: © Copyright 1998 American Mathematical Society