{
  "id": "math/0511267",
  "version": "v2",
  "published": "2005-11-10T14:44:31.000Z",
  "updated": "2006-04-18T10:02:45.000Z",
  "title": "On the Picard group of low-codimension subvarieties",
  "authors": [
    "Enrique Arrondo",
    "Jorge Caravantes"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n − 2 inherit the Picard group from the ambient space (as it happens when the ambient space is a projective space, according to results of Barth and Larsen). As an application, we give an affirmative answer (up to some mild natural numerical conditions) when the ambient space is a Grassmannian of lines (thus improving results of Barth, Van de Ven and Sommese) or a product of two projective spaces of the same dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-18T10:02:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C22"
    ],
    "keywords": [
      "picard group",
      "low-codimension subvarieties",
      "ambient space",
      "mild natural numerical conditions",
      "projective space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11267A"
    }
  }
}