{
  "id": "1507.04442",
  "version": "v1",
  "published": "2015-07-16T03:50:42.000Z",
  "updated": "2015-07-16T03:50:42.000Z",
  "title": "K-Stability for Varieties with Torus Action",
  "authors": [
    "Nathan Ilten",
    "Hendrik Süß"
  ],
  "comment": "19 pages, 5 figures",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Sz\\'ekelyhidi, we effectively determine the existence of K\\\"ahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of K\\\"ahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial K\\\"ahler-Ricci soliton.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-16T03:50:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q20",
      "14L30",
      "14J45"
    ],
    "keywords": [
      "fano threefolds",
      "algebraic torus action",
      "fano manifolds",
      "equivariant k-stability",
      "general orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150704442I"
    }
  }
}