Automorphism Groups of Cyclic p-gonal Pseudo-real Riemann Surfaces

Abstract

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 $C_n⋉C_p$ 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 some real 2-manifolds embbeded in the branch locus of moduli space.