Original scientific paper

https://doi.org/10.3336/gm.60.2.06

Real equations for o–extremal Riemann surfaces with abelian automorphism groups

Ewa Kozłowska-Walania ; Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Peter Turbek ; Department of Mathematics and Statistics, Purdue University Northwest, 2200 169th Street, Hammond, Indiana, 46323

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Abstract

It is well known that the fixed point set of a Riemann surface of genus \(g\) under the action of a symmetry is either empty or consists of a disjoint set of at most \(g+1\) ovals. Bounds on the total number of fixed ovals given by a set of \(k\) non-conjugate symmetries are known. In this paper, for \(k \ge 4\), we calculate all the possible topological types of symmetries in such a maximal configuration, provided that the symmetries commute. We also find real equations for the Riemann surfaces that achieve these bounds where the symmetries are expressed as complex conjugation.

Keywords

Riemann surface, symmetry of a Riemann surface, real form, automorphisms of Riemann surface, equations for Riemann surfaces, Fuchsian groups, Riemann uniformization theorem

Hrčak ID:

342483

URI

https://hrcak.srce.hr/342483

Publication date:

20.7.2026.

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