{
  "id": "2010.13135",
  "version": "v1",
  "published": "2020-10-25T15:23:00.000Z",
  "updated": "2020-10-25T15:23:00.000Z",
  "title": "Moduli dimensions of lattice polygons",
  "authors": [
    "Marino Echavarria",
    "Max Everett",
    "Shinyu Huang",
    "Liza Jacoby",
    "Ralph Morrison",
    "Ayush Kumar Tewari",
    "Raluca Vlad",
    "Ben Weber"
  ],
  "comment": "17 pages, 15 figures",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "Given a lattice polygon $P$ with $g$ interior lattice points, we associate to it the moduli space of tropical curves of genus $g$ with Newton polygon $P$. We completely classify the possible dimensions such a moduli space can have. For non-hyperelliptic polygons the dimension must be between $g$ and $2g+1$, and can take on any integer value in this range, with exceptions only in the cases of genus $3$, $4$, and $7$. We provide a similar result for hyperelliptic polygons, for which the range of dimensions is from $g$ to $2g-1$. In the case of non-hyperelliptic polygons, our results also hold for the moduli space of algebraic curves that are non-degenerate with respect to $P$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-25T15:23:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14T05",
      "52B20",
      "14H10"
    ],
    "keywords": [
      "lattice polygon",
      "moduli dimensions",
      "moduli space",
      "non-hyperelliptic polygons",
      "interior lattice points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}