{
  "id": "math/0602258",
  "version": "v2",
  "published": "2006-02-13T19:45:21.000Z",
  "updated": "2006-02-16T18:12:45.000Z",
  "title": "A Counterexample to King's Conjecture",
  "authors": [
    "Lutz Hille",
    "Markus Perling"
  ],
  "comment": "15 pages, 4 figures, requires packages ams*, enumerate, graphicx, citation corrected",
  "journal": "Compos. Math. 142, No. 6, 1507-1521 (2006)",
  "categories": [
    "math.AG",
    "hep-th"
  ],
  "abstract": "King's conjecture states that on every smooth complete toric variety $X$ there exists a strongly exceptional collection which generates the bounded derived category of $X$ and which consists of line bundles. We give a counterexample to this conjecture. This example is just the Hirzebruch surface $\\mathbb{F}_2$ iteratively blown up three times, and we show by explicit computation of cohomology vanishing that there exist no strongly exceptional sequences of length 7.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-16T18:12:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "18E30",
      "14J81"
    ],
    "keywords": [
      "counterexample",
      "smooth complete toric variety",
      "kings conjecture states",
      "strongly exceptional collection",
      "line bundles"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 710546,
      "adsabs": "2006math......2258H"
    }
  }
}