{
  "id": "2007.14320",
  "version": "v1",
  "published": "2020-07-28T15:42:28.000Z",
  "updated": "2020-07-28T15:42:28.000Z",
  "title": "K-stability of cubic fourfolds",
  "authors": [
    "Yuchen Liu"
  ],
  "comment": "19 pages. Comments welcome",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the corresponding GIT stabilities, which was studied in detail by Laza. In particular, this implies that all smooth cubic fourfolds admit K\\\"ahler-Einstein metrics. Key ingredients are local volume estimates in dimension three due to Liu-Xu, and Ambro-Kawamata's non-vanishing theorem for Fano fourfolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-28T15:42:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "k-stability",
      "smooth cubic fourfolds admit",
      "git moduli space",
      "cubic fourfolds coincide",
      "local volume estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}