{
  "id": "math/0110259",
  "version": "v4",
  "published": "2001-10-23T21:25:03.000Z",
  "updated": "2005-05-02T08:51:14.000Z",
  "title": "Rank 4 vector bundles on the quintic threefold",
  "authors": [
    "C. Madonna"
  ],
  "comment": "v2: 8 pages. Title changed. One wrong example is removed. More explicit examples are given - v3: typos corrected according to referees suggestions - v.4 final version, to appear on Central European Journal of Mathematics",
  "journal": "CEJM 3(3) 2005, 404-411",
  "categories": [
    "math.AG"
  ],
  "abstract": "By the results of the author and Chiantini in Math.AG/0110102, on a general quintic threefold $X \\subset {\\mathbf P}^4$ the minimum integer $p$ for which there exists a positive dimensional family of irreducible rank $p$ vector bundles on $X$ without intermediate cohomology is at least three. In this paper we show that $p \\leq 4$, by constructing series of positive dimensional families of rank 4 vector bundles on $X$ without intermediate cohomology. The general member of such family is an indecomposable bundle from the extension class $Ext^1(E,F)$, for a suitable choice of the rank 2 ACM bundles $E$ and $F$ on $X$. The existence of such bundles of rank $p = 3$ remains under question.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2005-05-02T08:51:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05"
    ],
    "keywords": [
      "vector bundles",
      "intermediate cohomology",
      "positive dimensional family",
      "general quintic threefold",
      "minimum integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10259M"
    }
  }
}