{
  "id": "1609.04573",
  "version": "v1",
  "published": "2016-09-15T11:28:12.000Z",
  "updated": "2016-09-15T11:28:12.000Z",
  "title": "Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects",
  "authors": [
    "Martí Lahoz",
    "Manfred Lehn",
    "Emanuele Macrì",
    "Paolo Stellari"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold in terms of moduli spaces of Gieseker stable sheaves. We show that the irreducible holomorphic symplectic eightfold associated to a cubic fourfold not containing a plane and described by the four authors is birational to a moduli space of stable aCM bundles on the cubic fourfold itself. For a very general such cubic fourfold, we show that the eightfold is isomorphic to a moduli space of tilt-stable objects in the derived category. Finally, the blow-up of this eightfold along the cubic fourfold is then described as a moduli space of rank 3 Gieseker stable torsion free sheaves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-15T11:28:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic fourfold",
      "moduli space",
      "generalized twisted cubics",
      "stable objects",
      "gieseker stable torsion free sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}