{
  "id": "1401.8050",
  "version": "v2",
  "published": "2014-01-31T02:57:05.000Z",
  "updated": "2015-01-29T20:02:17.000Z",
  "title": "Birational Geometry of the Space of Complete Quadrics",
  "authors": [
    "César Lozano Huerta"
  ],
  "comment": "20 pages, 1 figure. To appear in International Mathematics Research Notices",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the birational geometry of the moduli space of complete $n$-quadrics $X$. We exhibit generators for Eff$(X)$ and Nef$(X)$, the cone of effective divisors and the cone of nef divisors, respectively. As a corollary X is a Mori Dream space. Furthermore, we run the MMP on $X$ and find a moduli interpretation for the models induced by the generators of the nef cone. In the case of complete quadric surfaces, we describe all the birational models of $X$ induced by the movable cone and find a moduli interpretation for some of these models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-31T02:57:05.000Z",
      "title": "Birational Geometry of Complete Quadrics",
      "abstract": "We study the birational geometry of the moduli space of complete $n$-quadrics $X$. We exhibit generators for Eff$(X)$ and Nef$(X)$, the cone of effective divisors and the cone of nef divisors, respectively. As a corollary X is a Mori Dream space. Furthermore, we run the MMP on $X$ and find a moduli interpretation for the models induced by the generators of the nef cone. For complete quadric surfaces, we describe all the birational models of $X$ induced by the movable cone and find a moduli interpretation for some of such models.",
      "comment": "20 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-29T20:02:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birational geometry",
      "moduli interpretation",
      "complete quadric surfaces",
      "mori dream space",
      "nef divisors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.8050L"
    }
  }
}