Geometrical study of prime order automorphisms on Klein surfaces

Abstract

We consider (n,q)-gonal Klein surfaces of algebraic genus p≥2 for which n≥p and n prime. We exclude the case n=2 corresponding to q-hyperelliptic surfaces, so n≥3. We study geometrical conditions on fundamental polygons of the NEC groups which uniformize these surfaces. From these conditions we give a way to construct such surfaces and obtain parameters which characterize them.