{
  "id": "1109.6368",
  "version": "v2",
  "published": "2011-09-28T23:27:43.000Z",
  "updated": "2012-02-17T04:09:07.000Z",
  "title": "Singularities of Cox Rings of Fano Varieties",
  "authors": [
    "Morgan V. Brown"
  ],
  "comment": "15 pages, 2 tikz figures. Added log Fano and log Calabi-Yau cases, and included an example of a non Cohen-Macaulay Cox ring due to Yoshinori Gongyo",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth complete Fano variety over $\\mathbb{C}$. We show that the Cox ring $\\bigoplus_{L\\in\\text{Pic}(X)}H^0(X,\\mathcal{O}_X(L))$ is Gorenstein with canonical singularities.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-17T04:09:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14J45"
    ],
    "keywords": [
      "cox ring",
      "smooth complete fano variety",
      "gorenstein",
      "canonical singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6368B"
    }
  }
}