{
  "id": "0908.0846",
  "version": "v2",
  "published": "2009-08-06T11:41:16.000Z",
  "updated": "2010-10-18T11:44:49.000Z",
  "title": "Derived category of toric fibrations",
  "authors": [
    "L. Costa",
    "S. Di Rocco",
    "R. M. Miro-Roig"
  ],
  "comment": "The main result of this paper proves the final conjecture that generalizes the results contained in arXiv:0908.0846",
  "categories": [
    "math.AG"
  ],
  "abstract": "The derived category of bounded complexes of coherent sheaves is one of the most important algebraic invariants of a smooth projective variety. An important approach to understand derived categories is to construct full strongly exceptional sequences. The problem of characterizing smooth projective varieties which have a full strongly exceptional collection and investigate whether there is one consisting of line bundles is a classical and important question in Algebraic Geometry. Not all smooth projective varieties have a full strongly exceptional collection of coherent sheaves. In this paper we give a structure theorem for the derived category of a toric fiber bundle X over Z with fiber F provided that F and Z have both a full strongly exceptional collection of line bundles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-18T11:44:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05"
    ],
    "keywords": [
      "derived category",
      "full strongly exceptional collection",
      "smooth projective variety",
      "toric fibrations",
      "line bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0846C"
    }
  }
}