{
  "id": "1103.0114",
  "version": "v2",
  "published": "2011-03-01T09:36:22.000Z",
  "updated": "2011-09-15T08:37:53.000Z",
  "title": "Embeddings of SL(2,Z) into the Cremona group",
  "authors": [
    "Jérémy Blanc",
    "Julie Déserti"
  ],
  "comment": "to appear in Transformation Groups",
  "journal": "Transform. Groups 17 (2012), no. 1, 21-50",
  "doi": "10.1007/s00031-012-9174-9",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing-up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of infinite order are hyperbolic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-15T08:37:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E07",
      "14L30",
      "15B36"
    ],
    "keywords": [
      "cremona group",
      "hyperbolic elements",
      "infinite order",
      "send elliptic",
      "dynamic properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0114B"
    }
  }
}