{
  "id": "1309.3695",
  "version": "v2",
  "published": "2013-09-14T19:37:13.000Z",
  "updated": "2013-09-26T20:00:20.000Z",
  "title": "Pseudo-automorphisms with no invariant foliation",
  "authors": [
    "Eric Bedford",
    "Serge Cantat",
    "Kyounghee Kim"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this provides a negative answer to a question of Guedj. On our way, we develop several techniques to study foliations which are invariant under birational transformations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-26T20:00:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "32H50",
      "14E07"
    ],
    "keywords": [
      "invariant foliation",
      "pseudo-automorphisms",
      "birational transformation",
      "second dynamical degrees coincide",
      "study foliations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3695B"
    }
  }
}