{
  "id": "1301.4538",
  "version": "v1",
  "published": "2013-01-19T08:05:59.000Z",
  "updated": "2013-01-19T08:05:59.000Z",
  "title": "Towards a criterion for slope stability of Fano manifolds along divisors",
  "authors": [
    "Kento Fujita"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We give a simple criterion for slope stability of Fano manifolds $X$ along divisors or smooth subvarieties. As an application, we show that $X$ is slope stable along an ample effective divisor $D\\subset X$ unless $X$ is isomorphic to a projective space and $D$ is a hyperplane section. We also give counterexamples to Aubin's conjecture on the relation between the anticanonical volume and the existence of a K\\\"ahler-Einstein metric. Finally, we consider the case that $\\dim X=3$; we give a complete answer for slope (semi)stability along divisors of Fano threefolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-19T08:05:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14L24",
      "32Q20"
    ],
    "keywords": [
      "fano manifolds",
      "slope stability",
      "ample effective divisor",
      "simple criterion",
      "fano threefolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4538F"
    }
  }
}