Cyclic $n$-gonal Surfaces

Abstract

A cyclic $n$-gonal surface is a compact Riemann surface $X$ of genus $g\ge 2$ admitting a cyclic group of conformal automorphisms $C$ of order $n$ such that the quotient space $X/C$ has genus 0. In this paper, we provide an overview of ongoing research into automorphism groups of cyclic $n$-gonal surfaces. Much of the paper is expository or will appear in forthcoming papers, so proofs are usually omitted. Numerous explicit examples are presented illustrating the computational methods currently being used to study these surfaces.

38 pages. This paper is based upon two lectures on the authors' joint work, presented by the first author at the UNED (Universidad Nacional de Educacion a Distancia) Geometry Seminar in February-March, 2009.

References in corpus (1)

• The Full Automorphism Group of a Cyclic $p$-gonal Surface