Riemann surfaces with maximal real symmetry

JOURNAL OF ALGEBRA

卷:443

Article

Bujalance, E.¹  Cirre, F. J.¹  Conder, M. D. E.² 

[1] UNED, Fac Ciencias, Dept Matemat Fundamentales, Madrid 28040, Spain

[2] Univ Auckland, Dept Math, Auckland 1142, New Zealand

关键词: Riemann surface;    Klein surface;    Automorphisms;    Symmetry type;   

DOI  :  10.1016/j.jalgebra.2015.05.015

来源: Elsevier

【 摘 要 】

Let S be a compact Riemann surface of genus g > 1, and let tau : S -> S be any anti-conformal automorphism of S, of order 2. Such an anti-conformal involution is known as a symmetry of S, and the species of all conjugacy classes of all symmetries of S constitute what is known as the symmetry type of S. The surface S is said to have maximal real symmetry if it admits a symmetry tau : S -> such that the compact Klein surface S/tau has maximal symmetry (which means that S/tau has the largest possible number of automorphisms with respect to its genus). If tau has fixed points, which is the only case we consider here, then the maximum number of automorphisms of S/tau is 12(g - 1). In the first part of this paper, we develop a computational procedure to compute the symmetry type of every Riemann surface of genus g with maximal real symmetry, for given small values of g > 1. We have used this to find all of them for 1 < g <= 101, and give details for 1 < g <= 25 (in an appendix). In the second part, we determine the symmetry types of four infinite families of Riemann surfaces with maximal real symmetry. We also determine the full automorphism group of the Klein surface S/tau associated with each symmetry tau : S -> S. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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