{
  "id": "1010.2002",
  "version": "v1",
  "published": "2010-10-11T05:44:20.000Z",
  "updated": "2010-10-11T05:44:20.000Z",
  "title": "Lengths of chains of minimal rational curves on Fano manifolds",
  "authors": [
    "Kiwamu Watanabe"
  ],
  "comment": "16 pages. To appear in Journal of Algebra",
  "journal": "Journal of Algebra Volume 325, Issue 1, 1 January 2011, Pages 163-176",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we consider a natural question how many minimal rational curves are needed to join two general points on a Fano manifold X of Picard number 1. In particular, we study the minimal length of such chains in the cases where the dimension of X is at most 5, the coindex of X is at most 3 and X equips with a structure of a double cover. As an application, we give a better bound on the degree of Fano 5-folds of Picard number 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-11T05:44:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "14J45",
      "14N99"
    ],
    "keywords": [
      "minimal rational curves",
      "fano manifold",
      "picard number",
      "better bound",
      "general points"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.2002W"
    }
  }
}