Cyclic $n$-gonal Surfaces

S. Allen Broughton; Aaron Wootton

Cyclic $n$-gonal Surfaces

Algebraic Geometry 2010-03-18 v1

Authors: S. Allen Broughton , Aaron Wootton

Abstract

A cyclic $n$ -gonal surface is a compact Riemann surface $X$ of genus $g\geq 2$ 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.

Keywords

automorphisms of algebraic surfaces mapping class groups mapping class groups of surfaces

Cite

@article{arxiv.1003.3262,
  title  = {Cyclic $n$-gonal Surfaces},
  author = {S. Allen Broughton and Aaron Wootton},
  journal= {arXiv preprint arXiv:1003.3262},
  year   = {2010}
}

Comments

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.

Cyclic $n$-gonal Surfaces

Abstract

Keywords

Cite

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