{
  "id": "1303.6998",
  "version": "v3",
  "published": "2013-03-27T22:47:52.000Z",
  "updated": "2015-02-08T14:51:05.000Z",
  "title": "ACM bundles on cubic fourfolds containing a plane",
  "authors": [
    "Martí Lahoz",
    "Emanuele Macrì",
    "Paolo Stellari"
  ],
  "comment": "18 pages. This is the last section of the previous version of arXiv:1303.6998 which is now spit into two parts. To appear in the Proceedings of the AIM workshop \"Brauer groups and obstruction problems: moduli spaces and arithmetic\" (Palo Alto, 2013)",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov's treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3 surface naturally associated to the fourfold as a moduli space of Gieseker stable ACM bundles of rank four.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-15T19:32:28.000Z",
      "title": "ACM bundles on cubic threefolds and fourfolds containing a plane",
      "abstract": "We study ACM bundles on cubic threefolds and fourfolds containing a plane. For this purpose, we propose a new approach based on derived category techniques. In the case of cubic threefolds, these techniques allow us to show that the moduli space of Ulrich bundles is always non-empty. Applied to cubic fourfolds containing a plane, they give us a way to recover the K3 surface naturally associated to the fourfold as a moduli space of stable ACM bundles of rank four.",
      "comment": "52 pages. Major revision: corrected the statement of Theorem A, added details to the proofs and exposition improved",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-08T14:51:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic threefolds",
      "fourfolds containing",
      "moduli space",
      "study acm bundles",
      "stable acm bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6998L"
    }
  }
}