{
  "id": "1611.05823",
  "version": "v1",
  "published": "2016-11-17T19:18:16.000Z",
  "updated": "2016-11-17T19:18:16.000Z",
  "title": "Characterization of projective spaces and $\\mathbb P^r$-bundles as ample divisors",
  "authors": [
    "Jie Liu"
  ],
  "comment": "13 pages, no figure. Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\\mathbb P^n$. As an application, we derive the classification of projective manifolds containing a $\\mathbb P^r$-bundle as an ample divisor by the recent work of D.~Litt.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-17T19:18:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M20",
      "14J40",
      "14J60",
      "14J70"
    ],
    "keywords": [
      "ample divisor",
      "projective spaces",
      "characterization",
      "projective manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}