{
  "id": "1605.05648",
  "version": "v1",
  "published": "2016-05-18T16:29:44.000Z",
  "updated": "2016-05-18T16:29:44.000Z",
  "title": "Gushel-Mukai varieties: linear spaces and periods",
  "authors": [
    "Olivier Debarre",
    "Alexander Kuznetsov"
  ],
  "comment": "39 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic fourfold and the primitive second cohomology of its variety of lines, a smooth hyperk\\\"ahler fourfold, are isomorphic as polarized integral Hodge structures. We prove analogous statements for smooth complex Gushel-Mukai varieties of dimension 4 (resp. 6), i.e., smooth dimensionally transverse intersections of the cone over the Grassmannian Gr(2,5), a quadric, and two hyperplanes (resp. of the cone over Gr(2,5) and a quadric). The associated hyperk\\\"ahler fourfold is in both cases a smooth double cover of a hypersurface in ${\\bf P}^5$ called an EPW sextic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-18T16:29:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14J35",
      "14J40",
      "14M15"
    ],
    "keywords": [
      "linear spaces",
      "smooth complex cubic fourfold",
      "smooth complex gushel-mukai varieties",
      "smooth dimensionally transverse intersections",
      "polarized integral hodge structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}