# Minimal genus of Klein surfaces admitting an automorphism of a given order

### Impacto

Bujalance, E. and Etayo Gordejuela, J. Javier and Gamboa, J. M. and Martens, Gerriet (1989) Minimal genus of Klein surfaces admitting an automorphism of a given order. Archiv der Mathematik, 52 (2). pp. 191-202. ISSN 0003-889X

## Abstract

Let K be a compact Klein surface of algebraic genus $g\ge 2,$ which is not a classical Riemann surface. The authors show that if K admits an automorphism of order $N>2,$ then it must have algebraic genus at least $(p\sb 1-1)N/p\sb 1$ if N is prime or if its smallest prime factor, $p\sb 1$, occurs with exponent 1 in N. Otherwise the genus is at least $(p\sb 1-1)(N/p\sb 1-1)$. This result extends to bordered Klein surfaces a result of {\it E. Bujalance} [Pac. J. Math. 109, 279-289 (1983)] and is the analog for Klein surfaces of a result of {\it W. J. Harvey} [Q. J. Math., Oxf. II. Ser. 17, 86-97 (1966)] and, ultimately, of {\it A. Wiman} [Kongl. Svenska Vetenskaps-Akad. Handl., Stockholm 21, No.1 and No.3 (1895)].

Item Type: Article Classification theory of Riemann surfaces; Real ground fields; Curves; Fuchsian groups and their generalizations Sciences > Mathematics > Algebraic geometry 15779 27 Jun 2012 09:28 01 Mar 2016 18:23