{
  "id": "2210.09189",
  "version": "v1",
  "published": "2022-10-17T15:42:31.000Z",
  "updated": "2022-10-17T15:42:31.000Z",
  "title": "On the regularity of conical Calabi-Yau potentials",
  "authors": [
    "Tran-Trung Nghiem"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "Using pluripotential theory on degenerate Sasakian manifolds, we show that a locally bounded conical Calabi-Yau potential on a Fano cone is actually smooth on the regular locus. This work is motivated by a similar result obtained by R. Berman in the case where the cone is toric. Our proof is purely pluripotential and independent of any extra symmetry imposed on the cone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-17T15:42:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q20",
      "32Q25",
      "53C25",
      "35J96",
      "32U05",
      "32U20",
      "32U25",
      "32U35"
    ],
    "keywords": [
      "regularity",
      "degenerate sasakian manifolds",
      "locally bounded conical calabi-yau potential",
      "pluripotential theory",
      "fano cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}