{
  "id": "math/0411636",
  "version": "v1",
  "published": "2004-11-29T16:51:01.000Z",
  "updated": "2004-11-29T16:51:01.000Z",
  "title": "The splitting criterion of Kempf and the Babylonian tower theorem",
  "authors": [
    "Iustin Coanda",
    "Guenther Trautmann"
  ],
  "comment": "LateX2e, 4 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that the idea used by Kempf (1990) in order to obtain a splitting criterion for vector bundles on projective spaces leads to an elementary proof of the Babylonian tower theorem for this class of bundles, a result due to Barth--Van de Ven (1974) in the rank 2 case and to Sato (1977) and Tyurin (1976) in the case of arbitrary rank. As a byproduct we obtain a slight improvement of the numerical criterion of Flenner (1985) in the particular case under consideration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-29T16:51:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14J60"
    ],
    "keywords": [
      "babylonian tower theorem",
      "splitting criterion",
      "arbitrary rank",
      "elementary proof",
      "vector bundles"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11636C"
    }
  }
}