On non-orientable Riemann surfaces with 2p or 2p + 2 automorphisms

Emilio Bujalance, Grzegorz Gromadzki and Peter Turbek

Vol. 201 (2001), No. 2, 267–288

DOI: 10.2140/pjm.2001.201.267

Abstract

It is known that the maximal order of a cyclic group of automorphisms admitted by a Klein surface or real algebraic curve of algebraic genus p is 2p or 2(p + 1), depending on whether p is odd or even. In this paper, we classify the automorphism groups of all non-orientable Klein surfaces, without boundary, which admit an automorphism group of order 2p, or 2(p + 1). We determine that the automorphism groups are cyclic precisely when the surfaces are hyperelliptic. Defining equations for all but one family of these Klein surfaces are given.

Milestones

Received: 10 January 2000

Revised: 7 July 2000

Published: 1 December 2001