{
  "id": "2010.03519",
  "version": "v1",
  "published": "2020-10-07T16:56:26.000Z",
  "updated": "2020-10-07T16:56:26.000Z",
  "title": "Compactifications of moduli of points and lines in the projective plane",
  "authors": [
    "Luca Schaffler",
    "Jenia Tevelev"
  ],
  "comment": "66 pages. Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Projective duality identifies the moduli spaces $\\mathbf{B}_n$ and $\\mathbf{X}(3,n)$ parametrizing linearly general configurations of $n$ points in $\\mathbb{P}^2$ and $n$ lines in the dual $\\mathbb{P}^2$, respectively. The space $\\mathbf{X}(3,n)$ admits Kapranov's Chow quotient compactification $\\overline{\\mathbf{X}}(3,n)$, studied also by Lafforgue, Hacking, Keel, Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of certain reducible degenerations of $\\mathbb{P}^2$ with $n$ \"broken lines\". Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing certain reducible degenerations of $\\mathbb{P}^2$ with $n$ smooth points. We investigate the relation between these approaches, answering a question of Kapranov from 2003.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-07T16:56:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J10",
      "14D06",
      "52C35",
      "52B40",
      "51E24",
      "14T05"
    ],
    "keywords": [
      "projective plane",
      "admits kapranovs chow quotient compactification",
      "compact moduli space",
      "reducible degenerations",
      "ksba moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}