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

Grzegorz Gromadzki , Ewa Kozłowska-Walania

Abstract

Given g ≥ 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.
Author Grzegorz Gromadzki (FMPI / IM)
Grzegorz Gromadzki,,
- Institute of Mathematics
, Ewa Kozłowska-Walania (FMPI / IM)
Ewa Kozłowska-Walania,,
- Institute of Mathematics
Journal seriesMoscow Mathematical Journal, ISSN 1609-3321, (A 25 pkt)
Issue year2018
Vol18
No3
Pages421-436
Publication size in sheets0.75
Keywords in Englishautomorphisms 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
Languageen angielski
Score (nominal)30
ScoreMinisterial score = 25.0, 30-10-2018, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 30-10-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.041 (2) - 2016=0.901 (5)
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