{
  "id": "1407.3658",
  "version": "v3",
  "published": "2014-07-14T14:06:57.000Z",
  "updated": "2016-01-26T08:48:25.000Z",
  "title": "Fano manifolds whose elementary contractions are smooth $\\mathbb P^1$-fibrations: A geometric characterization of flag varieties",
  "authors": [
    "Gianluca Occhetta",
    "Luis E. Solá Conde",
    "Kiwamu Watanabe",
    "Jarosław A. Wiśniewski"
  ],
  "comment": "30 pages, minor issues corrected. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze",
  "categories": [
    "math.AG"
  ],
  "abstract": "The present paper provides a geometric characterization of complete flag varieties for semisimple algebraic groups. Namely, if $X$ is a Fano manifold whose all elementary contractions are $\\mathbb P^1$-fibrations then $X$ is isomorphic to the complete flag manifold $G/B$ where $G$ is a semi-simple Lie algebraic group and $B$ is a Borel subgroup of $G$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-24T07:24:44.000Z",
      "title": "Fano manifolds whose elementary contractions are smooth $\\mathbb P^1$-fibrations",
      "comment": "30 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-01-26T08:48:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14E30",
      "14M17"
    ],
    "keywords": [
      "fano manifold",
      "elementary contractions",
      "fibrations",
      "semi-simple lie algebraic group",
      "complete flag varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3658O"
    }
  }
}