On Conjugacy of p-gonal Automorphisms of Riemann Surfaces

Abstract

that for g > (p - 1)2 , a p-gonal The classical Castelnuovo-Severi theorem implies automorphism group of a cyclic p-gonal Riemann surface X of genus g is unique. Here we deal with the case g (p - 1)2 ; we give a new and short proof of a result of Gonz´alez-Diez that a cyclic p-gonal Riemann surface of such genus has one conjugacy class of p-gonal automorphism groups in the group of automorphisms of X .