RMC - Vol. 10, Num. 2 - D. Singerman/P. Watson

Full paper in PDF:
$%D. Singerman and P. Watson, Non-maximal cyclic group actions on compact Riemann surfaces, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 2, 423–439.%$

Non-Maximal Cyclic Group Actions on Compact Riemann Surfaces

David SINGERMAN and Paul WATSON

Faculty of Mathematical Studies
University of Southampton
Southampton SO17 1BJ — UK

ds@maths.soton.ac.uk

Received: July 1, 1997
Revised: October 22, 1997

ABSTRACT

We say that a finite group $G$ of automorphisms of a Riemann surface $X$ is non-maximal in genus g if (i) $G$ acts as a group of automorphisms of some compact Riemann surface $Xg$ of genus $g$ and (ii), for all such surfaces $Xg$ , $|AutXg|> |G|$ . In this paper we investigate the case where $G$ is a cyclic group $Cn$ of order $n$ . If $Cn$ acts on only finitely many surfaces of genus $g$ , then we completely solve the problem of finding all such pairs $(n,g)$ .

1991 Mathematics Subject Classification: 20H10, 30F10.