Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Moscow Mathematical Journal

Volume 18, Issue 3, July–September 2018  pp. 421–436.

The Groups Generated by Maximal Sets of Symmetries of Riemann Surfaces and Extremal Quantities of their Ovals

Authors:  Grzegorz Gromadzki (1) and Ewa Kozłowska-Walania (1)
Author institution:(1) Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Summary: 

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.

2010 Math. Subj. Class. Primary: 30F99; Secondary: 14H37, 20F.



Keywords: 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.

Contents   Full-Text PDF