{
  "id": "1201.6246",
  "version": "v5",
  "published": "2012-01-30T15:12:34.000Z",
  "updated": "2013-07-22T09:18:28.000Z",
  "title": "Gonality of algebraic curves and graphs",
  "authors": [
    "Lucia Caporaso"
  ],
  "comment": "Final version to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthday",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We study the interplay between the classical theory of linear series on curves, and the recent theory of linear series on graphs. We prove that every d-gonal (weighted) graph of Hurwitz type is the dual graph of a d-gonal curve. Conversely the dual graph of a d-gonal curve is equivalent to a d-gonal graph. We define d-gonal graphs by what we call harmonic indexed morphisms. Generalizations to higher dimensional linear series, and applications to tropical curves and hyperelliptic graphs are given.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-07-22T09:18:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14H51",
      "14T05",
      "05C99"
    ],
    "keywords": [
      "algebraic curves",
      "d-gonal curve",
      "dual graph",
      "higher dimensional linear series",
      "define d-gonal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.6246C"
    }
  }
}