{
  "id": "math/9806153",
  "version": "v1",
  "published": "1998-06-29T12:00:45.000Z",
  "updated": "1998-06-29T12:00:45.000Z",
  "title": "Cyclic coverings and higher order embeddings of algebraic varieties",
  "authors": [
    "Thomas Bauer",
    "Sandra Di Rocco",
    "Tomasz Szemberg"
  ],
  "comment": "LATEX, 15 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "An algebraic variety X is embedded to the order k via a line bundle L if the global sections of L generate all (simultaneous) jets of order k on X or if they separate all zero-dimensional subschemes of length at most k+1. Even though we refer to both situations as \"higher order embeddings\", the first notion (in which case L is said to be k-jet ample) is stronger than the second one (when L is k-very ample). The purpose of this paper is to study higher order embeddings of cyclic coverings \\pi:Y\\to X via line bundles given by pulling back \"sufficiently positive\" line bundles on X. Given a line bundle L on X, we relate the order of the embedding defined by \\pi^*L to that of L and of certain rank 1 summands of the vector bundle L\\tensor\\pi_*\\calo_Y. As expected, the sufficient conditions for \\pi^*L to be k-jet ample are stronger then the ones needed in order for \\pi^*L to be k-very ample.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-06-29T12:00:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic variety",
      "cyclic coverings",
      "line bundle",
      "k-jet ample",
      "k-very ample"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......6153B"
    }
  }
}