{
  "id": "1906.01445",
  "version": "v1",
  "published": "2019-06-04T13:56:36.000Z",
  "updated": "2019-06-04T13:56:36.000Z",
  "title": "Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds",
  "authors": [
    "Igor Dolgachev",
    "Dimitri Markushevich"
  ],
  "comment": "62 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Fano models of Enriques surfaces in $\\mathbb P^5$. The first one parametrizes the varieties of lines on smooth cubic hypersurfaces containing 10 mutually intersecting planes. The second one is a family of double EPW sextics introduced by K. O'Grady. The EPW sextics are associated to Lagrangian subspaces of the Pl\\\"ucker space of the Grassmannian $G_2(\\mathbb P^5)$ spanned by 10 mutually intersecting planes in $\\mathbb P^5$. Also some results are obtained on the variety of general tens of mutually intersecting planes, not necessarily associated to Fano models of Enriques surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-04T13:56:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J35",
      "14J10",
      "14N20"
    ],
    "keywords": [
      "enriques surfaces",
      "holomorphic symplectic fourfolds",
      "lagrangian tens",
      "mutually intersecting planes",
      "epw sextics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}