{
  "id": "1005.2462",
  "version": "v2",
  "published": "2010-05-14T06:50:17.000Z",
  "updated": "2010-06-08T19:54:20.000Z",
  "title": "Normal singularities with torus actions",
  "authors": [
    "Alvaro Liendo",
    "Hendrik Süß"
  ],
  "comment": "23 pages",
  "journal": "Tohoku Math. J. (2) Volume 65, Number 1 (2013), 105-130",
  "doi": "10.2748/tmj/1365452628",
  "categories": [
    "math.AG"
  ],
  "abstract": "We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of X. In particular, we give criteria for X to have only rational, (QQ-)factorial, or (QQ-)Gorenstein singularities. We also give partial criteria for X to be Cohen-Macaulay or log-terminal. Finally, we provide a method to construct factorial affine varieties with a torus action. This leads to a full classification of such varieties in the case where the action is of complexity one.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-08T19:54:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14B05",
      "14M25"
    ],
    "keywords": [
      "torus action",
      "normal singularities",
      "construct factorial affine varieties",
      "normal affine variety",
      "gorenstein singularities"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.2462L"
    }
  }
}