{
  "id": "2002.03417",
  "version": "v1",
  "published": "2020-02-09T18:25:01.000Z",
  "updated": "2020-02-09T18:25:01.000Z",
  "title": "On the Kodaira dimension of the moduli space of hyperelliptic curves with marked points",
  "authors": [
    "Irene Schwarz"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "It is known that the moduli space $\\overline{\\mathcal{H}}_{g,n}$ of genus g stable hyperelliptic curves with $n$ marked points is uniruled for $n \\geq 4g+5$. In this paper we consider the complementary case and show that $\\overline{\\mathcal{H}}_{g,n}$ has non-negative Kodaira dimension for $n = 4g+6$ and is of general type for $n \\geq 4g+7$. Important parts of our proof are the calculation of the canonical divisor and establishing that the singularities of $\\overline{\\mathcal{H}}_{g,n}$ do not establish adjunction conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-09T18:25:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "marked points",
      "complementary case",
      "stable hyperelliptic curves",
      "non-negative kodaira dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}