Full paper in PDF:
$%D. Singerman and P. Watson, Non-maximal cyclic group actions on compact Riemann surfaces, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 2, 423439.%$

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

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.