{
  "id": "1605.04680",
  "version": "v1",
  "published": "2016-05-16T09:05:54.000Z",
  "updated": "2016-05-16T09:05:54.000Z",
  "title": "Extremal rays and nefness of tangent bundles",
  "authors": [
    "Akihiro Kanemitsu"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In view of Mori theory, rational homogenous manifolds satisfy a recursive condition: every elementary contraction is a rational homogeneous fibration and the image of any elementary contraction also satisfies the same property. In this paper, we show that a smooth Fano $n$-fold with the same condition and Picard number greater than $n-6$ is either a rational homogeneous manifold or the product of $n-7$ copies of $\\mathbb{P}^1$ and a Fano $7$-fold $X_0$ constructed by G. Ottaviani. We also clarify that $X_0$ has non-nef tangent bundle and in particular is not rational homogeneous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-16T09:05:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14J40",
      "14M17"
    ],
    "keywords": [
      "extremal rays",
      "elementary contraction",
      "non-nef tangent bundle",
      "picard number greater",
      "rational homogenous manifolds satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}