{
  "id": "1212.5083",
  "version": "v2",
  "published": "2012-12-20T15:27:36.000Z",
  "updated": "2015-01-09T00:01:18.000Z",
  "title": "Locally unsplit families of rational curves of large anticanonical degree on Fano manifolds",
  "authors": [
    "Cinzia Casagrande",
    "Stéphane Druel"
  ],
  "comment": "34 pages, 2 figures, to appear in IMRN",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we address Fano manifolds X with a locally unsplit dominating family of rational curves of anticanonical degree equal to the dimension of X. We first observe that their Picard number is at most 3, and then we provide a classification of all cases with maximal Picard number. We also give examples of locally unsplit dominating families of rational curves whose varieties of minimal tangents at a general point is singular.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-20T15:27:36.000Z",
      "comment": "34 pages, 2 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-09T00:01:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14C05",
      "14E30"
    ],
    "keywords": [
      "rational curves",
      "large anticanonical degree",
      "locally unsplit families",
      "locally unsplit dominating family",
      "address fano manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5083C"
    }
  }
}