{
  "id": "math/0410584",
  "version": "v1",
  "published": "2004-10-27T21:56:15.000Z",
  "updated": "2004-10-27T21:56:15.000Z",
  "title": "Rational curves of minimal degree and characterizations of ${\\mathbb P}^n$",
  "authors": [
    "Carolina Araujo"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we investigate complex uniruled varieties $X$ whose rational curves of minimal degree satisfy a special property. Namely, we assume that the tangent directions to such curves at a general point $x\\in X$ form a linear subspace of $T_xX$. As an application of our main result, we give a unified geometric proof of Mori's, Wahl's, Campana-Peternell's and Andreatta-Wi\\'sniewski's characterizations of ${\\mathbb P}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-27T21:56:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E08",
      "14J40"
    ],
    "keywords": [
      "rational curves",
      "minimal degree satisfy",
      "unified geometric proof",
      "complex uniruled varieties",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10584A"
    }
  }
}