The groups generated by maximal sets of symmetries of Riemann surfaces and extremal quantities of their ovals
Grzegorz Gromadzki , Ewa Kozłowska-Walania
AbstractGiven 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.
|Journal series||Moscow Mathematical Journal, ISSN 1609-3321, (A 25 pkt)|
|Publication size in sheets||0.75|
|Keywords in English||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|
|Score|| = 25.0, ArticleFromJournal|
= 30.0, ArticleFromJournal
|Publication indicators||: 2017 = 0.704 (2) - 2017=1.0 (5)|
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