{
  "id": "1007.5364",
  "version": "v2",
  "published": "2010-07-30T03:54:20.000Z",
  "updated": "2012-02-09T14:28:59.000Z",
  "title": "Reduced Divisors and Embeddings of Tropical Curves",
  "authors": [
    "Omid Amini"
  ],
  "comment": "Final version (to appear in Trans. Amer. Math. Soc.), 29 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Given a divisor $D$ on a tropical curve $\\Gamma$, we show that reduced divisors define an integral affine map from the tropical curve to the complete linear system $|D|$. This is done by providing an explicit description of the behavior of reduced divisors under infinitesimal modifications of the base point. We consider the cases where the reduced-divisor map defines an embedding of the curve into the linear system, and in this way, classify all the tropical curves with a very ample canonical divisor. As an application of the reduced-divisor map, we show the existence of Weierstrass points on tropical curves of genus at least two and present a simpler proof of a theorem of Luo on rank-determining sets of points. We also discuss the classical analogue of the (tropical) reduced-divisor map: For a smooth projective curve $C$ and a divisor $D$ of non-negative rank on $C$, reduced divisors equivalent to $D$ define a morphism from $C$ to the complete linear system $|D|$, which is described in terms of Wronskians.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-09T14:28:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tropical curve",
      "complete linear system",
      "integral affine map",
      "reduced-divisor map defines",
      "explicit description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.5364A"
    }
  }
}