{
  "id": "1003.3973",
  "version": "v2",
  "published": "2010-03-21T07:17:05.000Z",
  "updated": "2013-02-23T11:53:39.000Z",
  "title": "Birational contraction of genus two tails in the moduli space of genus four curves I",
  "authors": [
    "Donghoon Hyeon",
    "Yongnam Lee"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that for $\\alpha \\in (2/3, 7/10)$, the log canonical model $\\bar M_4(\\alpha)$ of the pair $(\\bar M_4, \\alpha \\delta)$ is isomorphic to the moduli space $\\bar M_4^{hs}$ of h-semistable curves, and that there is a birational morphism $\\Xi: \\bar M_4^{hs} \\to \\bar M_4(2/3)$ that contracts the locus of curves $C_1\\cup_p C_2$ consisting of genus two curves meeting in a node $p$ such that $p$ is a Weierstrass point of $C_1$ or $C_2$. To obtain this morphism, we construct a compact moduli space $\\bar M_{2,1}^{hs}$ of pointed genus two curves that have nodes, ordinary cusps and tacnodes as singularity, and prove that it is isomorphic to Rulla's flip constructed in his thesis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-23T11:53:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L24",
      "14H10"
    ],
    "keywords": [
      "birational contraction",
      "compact moduli space",
      "rullas flip",
      "log canonical model",
      "weierstrass point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3973H"
    }
  }
}