This article is cited in 2 papers

The groups generated by maximal sets of symmetries of Riemann surfaces and extremal quantities of their ovals

Grzegorz Gromadzki, Ewa Kozłowska-Walania

Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Abstract: Given $g\geq 2$, there are formulas for the maximal number of non-conjugate symmetries of a Riemann surface of genus $g$ and the maximal number of ovals for a given number of symmetries. Here we describe the algebraic structure of the automorphism groups of Riemann surfaces, supporting such extremal configurations of symmetries, showing that they are direct products of a dihedral group and some number of cyclic groups of order $2$. This allows us to establish a deeper relation between the mentioned above quantitative (the number of symmetries) and qualitative (configurations of ovals) cases.

Key words and phrases: automorphisms of Riemann surfaces, symmetric Riemann surfaces, real forms of complex algebraic curves, Fuchsian and NEC groups, ovals of symmetries of Riemann surfaces, separability of symmetries, Harnack–Weichold conditions.

MSC: Primary 30F99; Secondary 14H37, 20F

Language: English

DOI: 10.17323/1609-4514-2018-18-3-421-436

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