{
  "id": "1306.3497",
  "version": "v2",
  "published": "2013-06-14T19:57:42.000Z",
  "updated": "2014-12-25T14:27:27.000Z",
  "title": "The number of vertices of a tropical curve is bounded by its area",
  "authors": [
    "Tony Yue Yu"
  ],
  "comment": "Added a geometric interpretation of tropical area using Berkovich geometry (see Remark 1.8)",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We introduce the notion of tropical area of a tropical curve defined in an open subset of $\\mathbb R^n$. We prove that the number of vertices of a tropical curve is bounded by the area of the curve. The approach is totally elementary yet tricky. Our proof employs ideas from intersection theory in algebraic geometry. The result can be interpreted as the fact that the moduli space of tropical curves with bounded area is of finite type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-14T19:57:42.000Z",
      "abstract": "We prove that the number of vertices of a tropical curve defined in an open subset of a Euclidean space is bounded by the area of the curve. The approach is totally elementary yet tricky. Our proof uses some ideas from algebraic geometry by making analogies. The result can be interpreted as the fact that the moduli space of tropical curves with area bounded below a given value is of finite type.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-25T14:27:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14T05",
      "52B05"
    ],
    "keywords": [
      "tropical curve",
      "euclidean space",
      "finite type",
      "algebraic geometry",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3497Y"
    }
  }
}