{
  "id": "math/0703596",
  "version": "v2",
  "published": "2007-03-20T15:07:31.000Z",
  "updated": "2008-10-13T18:48:05.000Z",
  "title": "Ordinary holomorphic webs of codimension one",
  "authors": [
    "Vincent Cavalier",
    "Daniel Lehmann"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "The main change with respect to the previous version is a change of terminology : we call \"ordinary\" the webs previously called \"regular\". A holomorphic $d$-web of codimension one in dimension $n$ is \"ordinary\", if it satisfies to some condition of genericity. In dimension at least 3, any such web has a rank bounded from above by a number $\\pi'(n,d)$ strictly smaller than the bound $\\pi(n,d)$ of castelnuovo. This bound $\\pi'(n,d)$ is optimal. Moreover, for some $d$'s, the abelian relations are sections with vanishing covariant derivative of some bundle with a connection, the curvature of which generalizes the Blaschke curvature. In dimension 2, we recover results of H\\'enaut and Pantazi",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-13T18:48:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R25",
      "58A20"
    ],
    "keywords": [
      "ordinary holomorphic webs",
      "codimension",
      "main change",
      "abelian relations",
      "blaschke curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3596C"
    }
  }
}