{
  "id": "1309.7229",
  "version": "v3",
  "published": "2013-09-27T13:17:09.000Z",
  "updated": "2016-03-09T20:28:54.000Z",
  "title": "Extremal divisors on moduli spaces of rational curves with marked points",
  "authors": [
    "Morgan Opie"
  ],
  "comment": "New sections 6 and 7 include a proof of the covering family criterion for extremality, examples, and a discussion of obstructions to constructing \"large\" extremal families. Final version; to appear in the Michigan Mathematical Journal",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study effective divisors on $\\overline{M}_{0,n}$, focusing on hypertree divisors introduced by Castravet and Tevelev and the proper transforms of divisors on $\\overline{M}_{1,n-2}$ introduced by Chen and Coskun. Results include a database of hypertree divisor classes and closed formulas for Chen--Coskun divisor classes. We relate these two types of divisors, and from this construct extremal divisors on $\\overline{M}_{0,n}$ for $n \\geq 7$ that furnish counterexamples to the conjectural description of the effective cone of $\\overline{M}_{0,n}$ given by Castravet and Tevelev.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-15T19:28:41.000Z",
      "abstract": "We study effective divisors on $\\overline{M}_{0,n}$, focusing on hypertree divisors introduced by Castravet-Tevelev and the proper transforms of divisors on $\\overline{M}_{1,n-2}$ introduced by Chen-Coskun. Results include a database of hypertree divisor classes and closed formulas for Chen-Coskun divisor classes. We relate these two types of divisors, and from this construct extremal divisors on $\\overline{M}_{0,n}$ for $ n \\geq 7$ that furnish counterexamples to the conjectural description of the effective cone of $\\overline{M}_{0,n}$ given by Castravet-Tevelev.",
      "comment": "Typos corrected, introduction reorganized for v2",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-03-09T20:28:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational curves",
      "moduli spaces",
      "marked points",
      "hypertree divisor classes",
      "chen-coskun divisor classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7229O"
    }
  }
}