{
  "id": "1005.4310",
  "version": "v3",
  "published": "2010-05-24T11:13:12.000Z",
  "updated": "2011-03-10T08:09:36.000Z",
  "title": "Slopes of smooth curves on Fano manifolds",
  "authors": [
    "Jun-Muk Hwang",
    "Hosung Kim",
    "Yongnam Lee",
    "Jihun Park"
  ],
  "comment": "13 pages, Theorems in the original version were modified. This paper will be published in the Bulletin of the London Mathematical Society",
  "doi": "10.1112/blms/bdr020",
  "categories": [
    "math.AG"
  ],
  "abstract": "Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\\\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension $n\\geq 3$ with respect to smooth curves. The question turns out to be easy for curves of genus $\\geq 1$ and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold $(X, -K_X)$ is not slope stable with respect to a smooth curve. Our result also states that a Fano threefold $X$ with Picard number 1 is slope stable with respect to every smooth curve unless $X$ is the projective space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-10T08:09:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14L24"
    ],
    "keywords": [
      "smooth curve",
      "slope stability",
      "main result classifies",
      "constant scalar curvature",
      "smooth rational curves"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4310H"
    }
  }
}