{
  "id": "1709.10198",
  "version": "v1",
  "published": "2017-09-28T23:29:28.000Z",
  "updated": "2017-09-28T23:29:28.000Z",
  "title": "Balanced complexes and effective divisors on $\\overline{M}_{0,n}$",
  "authors": [
    "José Luis González",
    "Elijah Gunther",
    "Olivia Zhang"
  ],
  "comment": "10 pages, 8 figures",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "Doran, Jensen and Giansiracusa showed a bijection between homogeneous elements in the Cox ring of $\\overline{M}_{0,n}$ not divisible by any exceptional divisor section, and weighted pure-dimensional simplicial complexes satisfying a zero-tension condition. Motivated by the study of the monoid of effective divisors, the pseudoeffective cone and the Cox ring of $\\overline{M}_{0,n}$, we point out a simplification of the zero-tension condition and study the space of balanced complexes. We give examples of irreducible elements in the monoid of effective divisors of $\\overline{M}_{0,n}$ for large $n$. In the case of $\\overline{M}_{0,7}$, we classify all such irreducible elements arising from nonsingular complexes and give an example of how irreducibility can be shown in the singular case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-28T23:29:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14H10",
      "05E45"
    ],
    "keywords": [
      "effective divisors",
      "balanced complexes",
      "zero-tension condition",
      "exceptional divisor section",
      "irreducible elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}