{
  "id": "math/0503161",
  "version": "v2",
  "published": "2005-03-08T19:00:18.000Z",
  "updated": "2006-01-12T18:48:48.000Z",
  "title": "On varieties which are uniruled by lines",
  "authors": [
    "A. L. Knutsen",
    "C. Novelli",
    "A. Sarti"
  ],
  "comment": "19 pages. Corrected version: lemma 2.2 in the previous version removed and substitued by lemma 2.3 in the new version",
  "categories": [
    "math.AG"
  ],
  "abstract": "Using the $\\sharp$-minimal model program of uniruled varieties we show that for any pair $(X, \\H)$ consisting of a reduced and irreducible variety $X$ of dimension $k \\geq 3$ and a globally generated big line bundle $\\H$ on $X$ with $d:= \\H^k$ and $n:= h^0(X, \\H)-1$ such that $d<2(n-k)-4$, then $X$ is uniruled of $\\H$-degree one, except if $(k,d,n)=(3,27,19)$ and a ${\\sharp}$-minimal model of $(X, \\H)$ is $(\\PP^3,\\O_{\\PP^3}(3))$. We also show that the bound is optimal for threefolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-01-12T18:48:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "14J30",
      "14J40",
      "14N25",
      "14C20",
      "14H45"
    ],
    "keywords": [
      "minimal model program",
      "globally generated big line bundle",
      "uniruled varieties",
      "irreducible variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3161K"
    }
  }
}