{
  "id": "1007.3327",
  "version": "v3",
  "published": "2010-07-20T03:19:53.000Z",
  "updated": "2011-03-14T04:39:30.000Z",
  "title": "The canonical module of a Cox ring",
  "authors": [
    "Mitsuyasu Hashimoto",
    "Kazuhiko Kurano"
  ],
  "comment": "19 pages, corrected minor errors and updated the references",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "In this paper, we shall describe the graded canonical module of a Noetherian multi-section ring of a normal projective variety. In particular, in the case of the Cox ring, we prove that the graded canonical module is a graded free module of rank one with the shift of degree $K_X$. We shall give two kinds of proofs. The first one utilizes the equivariant twisted inverse functor developed by the first author. The second proof is down-to-earth, that avoids the twisted inverse functor.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-14T04:39:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "13C20"
    ],
    "keywords": [
      "cox ring",
      "graded canonical module",
      "normal projective variety",
      "equivariant twisted inverse functor",
      "graded free module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.3327H"
    }
  }
}