{
  "id": "0905.4647",
  "version": "v2",
  "published": "2009-05-28T13:35:37.000Z",
  "updated": "2010-01-30T17:48:25.000Z",
  "title": "Group actions on affine cones",
  "authors": [
    "Takashi Kishimoto",
    "Yuri Prokhorov",
    "Mikhail Zaidenberg"
  ],
  "comment": "41p",
  "categories": [
    "math.AG"
  ],
  "abstract": "We address the following question: Determine the affine cones over smooth projective varieties which admit an action of a connected algebraic group different from the standard C*-action by scalar matrices and its inverse action. We show in particular that the affine cones over anticanonically embedded smooth del Pezzo surfaces of degree at least 4 possess such an action. A question by Flenner and the third author whether this is also true for cubic surfaces, occurs to be out of reach for our methods. Nevertheless, we provide a general geometric criterion that could be helpful also in this case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-30T17:48:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "13A50",
      "14L30"
    ],
    "keywords": [
      "affine cones",
      "group actions",
      "embedded smooth del pezzo surfaces",
      "anticanonically embedded smooth del pezzo",
      "general geometric criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4647K"
    }
  }
}