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This article is cited in 1 scientific paper (total in 1 paper)
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.
Citation:
Grzegorz Gromadzki, Ewa Kozłowska-Walania, “The groups generated by maximal sets of symmetries of Riemann surfaces and extremal quantities of their ovals”, Mosc. Math. J., 18:3 (2018), 421–436
Linking options:
https://www.mathnet.ru/eng/mmj681 https://www.mathnet.ru/eng/mmj/v18/i3/p421
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Abstract page: | 127 | References: | 25 |
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