{
  "id": "1003.3262",
  "version": "v1",
  "published": "2010-03-16T22:08:05.000Z",
  "updated": "2010-03-16T22:08:05.000Z",
  "title": "Cyclic $n$-gonal Surfaces",
  "authors": [
    "S. Allen Broughton",
    "Aaron Wootton"
  ],
  "comment": "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.",
  "categories": [
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-16T22:08:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H37",
      "30F20",
      "30F10"
    ],
    "keywords": [
      "gonal surface",
      "compact riemann surface",
      "cyclic group",
      "quotient space",
      "computational methods"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3262B"
    }
  }
}