{
  "id": "0709.4485",
  "version": "v4",
  "published": "2007-09-27T19:58:19.000Z",
  "updated": "2016-02-21T22:08:15.000Z",
  "title": "Rank of divisors on tropical curves",
  "authors": [
    "Jan Hladký",
    "Daniel Král'",
    "Serguei Norine"
  ],
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the Riemann-Roch theorem for tropical curves, similar to the recent proof of the Riemann-Roch theorem for graphs by Baker and Norine, is presented. In addition, a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to the rank of D on the corresponding metric graph is confirmed, and an algorithm for computing the rank of a divisor on a tropical curve is constructed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-05-25T19:24:35.000Z",
      "comment": "35 pages, errors pointed to us by Marc Coppens and an anonymous referee fixed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2016-02-21T22:08:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tropical curve",
      "riemann-roch theorem",
      "linear equivalence classes",
      "algorithmic properties",
      "purely combinatorial methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.4485H"
    }
  }
}