{
  "id": "1407.4445",
  "version": "v1",
  "published": "2014-07-16T19:54:30.000Z",
  "updated": "2014-07-16T19:54:30.000Z",
  "title": "The gonality conjecture on syzygies of algebraic curves of large degree",
  "authors": [
    "Lawrence Ein",
    "Robert Lazarsfeld"
  ],
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting that one can read off the gonality of a curve C from its resolution in the embedding defined by any one line bundle of sufficiently large degree. More generally, we establish a necessary and sufficient condition for the asymptotic vanishing of the weight one syzygies of the module associated to an arbitrary line bundle on C.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-16T19:54:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gonality conjecture",
      "algebraic curves",
      "arbitrary line bundle",
      "surprisingly quick proof",
      "second author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4445E"
    }
  }
}