On Conjugacy of p-gonal Automorphisms of Riemann Surfaces

The classical Castelnuovo-Severi theorem implies that for g> (p−1)2, a p-gonal 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 González-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. Key words: automorphisms of Riemann surfaces, fixed points, ramified coverings o