Automorphism groups of cyclic p-gonal pseudo-real Riemann surfaces

In this article we prove that the full automorphism group of a cyclic p-gonal pseudo-real Riemann surface of genus g is either a semidirect product C-n proportional to C-p or a cyclic group, where p is a prime > 2 and g > (p - 1)(2). We obtain necessary and sufficient conditions for the existence of a cyclic p-gonal pseudo-real Riemann surface with full automorphism group isomorphic to a given finite group. Finally we describe some families of cyclic p-gonal pseudo-real Riemann surfaces where the order of the full automorphism group is maximal and show that such families determine real 2-manifolds embedded in the branch locus of moduli space. (C) 2015 Elsevier Inc. All rights reserved.