{
  "id": "1508.03915",
  "version": "v1",
  "published": "2015-08-17T02:45:44.000Z",
  "updated": "2015-08-17T02:45:44.000Z",
  "title": "Birational contractions of $\\overline{\\mathrm{M}}_{0,n}$ and combinatorics of extremal assignments",
  "authors": [
    "Han-Bom Moon",
    "Charles Summers",
    "James von Albade",
    "Ranze Xie"
  ],
  "comment": "35 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a finite union of atomic extremal assignments. We discuss a connection with the birational geometry of the moduli space of stable pointed curves. As applications, we study three special classes of extremal assignments: smooth, toric, and invariant with respect to the symmetric group action. We identify them with three combinatorial objects: simple intersecting families, complete multipartite graphs, and special families of integer partitions, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-17T02:45:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14E05",
      "14E30",
      "05C05"
    ],
    "keywords": [
      "birational contractions",
      "combinatorics",
      "atomic extremal assignments",
      "pointed smooth rational curves",
      "symmetric group action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803915M"
    }
  }
}