The full automorphism group of a cyclic p-gonal surface

Abstract

If p is prime, a compact Riemann surface X of genus g ⩾ 2 is called cyclic p-gonal if it admits a cyclic group of automorphisms C p of order p such that the quotient space X / C p has genus 0. If in addition C p is not normal in the full automorphism A, then we call X a non-normal p-gonal surface. In the following we classify all non-normal p-gonal surfaces.