{
  "id": "2201.07037",
  "version": "v2",
  "published": "2022-01-18T15:03:44.000Z",
  "updated": "2022-02-05T12:49:38.000Z",
  "title": "On fibrations and measures of irrationality of hyper-Kähler manifolds",
  "authors": [
    "Claire Voisin"
  ],
  "comment": "The proof of the last proposition has been corrected and simplified",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove some results on the fibers and images of rational maps from a hyper-K\\\"ahler manifold. We study in particular the minimal genus of fibers of a fibration into curves. The last section of this paper is devoted to the study of the rational map defined by a linear system on a hyper-K\\\"ahler fourfold satisfying numerical conditions similar to those considered by O'Grady in his study of fourfolds numerically equivalent to $K3^{[2]}$. We extend his results to this more general context.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-05T12:49:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyper-kähler manifolds",
      "rational map",
      "irrationality",
      "fourfold satisfying numerical conditions similar",
      "general context"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}