On s-extremal Riemann surfaces of even genus

被引：0

作者：

Kozlowska-Walania, Ewa ^{[1
]}

机构：

[1] Univ Gdansk, Fac Math Phys & Informat, Inst Math, Wita Stwosza 57, PL-80952 Gdansk, Poland

来源：

REVISTA MATEMATICA COMPLUTENSE | 2022年 / 35卷 / 01期

关键词：

Riemann surface; Symmetry of a Riemann surface; Real form; Automorphisms of Riemann surface; Fuchsian groups; Riemann uniformization theorem; Separating symmetry; REAL FORMS; SYMMETRIES; AUTOMORPHISMS; THEOREM; OVALS;

D O I：

10.1007/s13163-020-00378-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Riemann surfaces of even genus g with the action of the group D-n x Z(2), with n even. These surfaces have the maximal number of 4 non-conjugate symmetries and shall be called s-extremal. We show various results for such surfaces, concerning the total number of ovals, topological types of symmetries, hyperellipticity degree and the minimal genus problem. If in addition an s-extremal Riemann surface has the maximal total number of ovals, then it shall simply be called extremal. In the main result of the paper we find all the families of extremal Riemann surfaces of even genera, depending on if one of the symmetries is fixed-point free or not.

引用

页码：159 / 178

页数：20

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