{
  "id": "0803.0179",
  "version": "v3",
  "published": "2008-03-03T05:21:47.000Z",
  "updated": "2010-02-23T04:58:30.000Z",
  "title": "Rank Two Sheaves on K3 Surfaces: A Special Construction",
  "authors": [
    "Colin Ingalls",
    "Madeeha Khalid"
  ],
  "comment": "Fixed various minor errors and reworked some arguments",
  "doi": "10.1093/qmath/has009",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of three quadrics, there is a natural correspondence between M and the moduli space M' of rank two vector bundles on X with Chern classes c_1=H and c_2=4. We build on previous work of Mukai and others, giving conditions and examples where M' is fine, compact, non-empty; and birational or isomorphic to M. We also present an explicit calculation of the Fourier-Mukai transform when X contains a line and has Picard number two.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-02-23T04:58:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J32"
    ],
    "keywords": [
      "k3 surface",
      "special construction",
      "sextic curve",
      "picard number",
      "complete intersection"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0179I"
    }
  }
}