{
  "id": "1205.4528",
  "version": "v2",
  "published": "2012-05-21T09:12:31.000Z",
  "updated": "2012-06-06T16:42:16.000Z",
  "title": "Noether-Lefschetz Theory with base locus",
  "authors": [
    "Vincenzo Di Gennaro",
    "Davide Franco"
  ],
  "comment": "18 pages, Added references",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $Z$ be a closed subscheme of a smooth complex projective variety $Y\\subseteq \\Ps^N$, with $\\dim\\,Y=2r+1\\geq 3$. We describe the intermediate N\\'eron-Severi group (i.e. the image of the cycle map $A_r(X)\\to H_{2r}(X;\\mathbb{Z})$) of a general smooth hypersurface $X\\subset Y$ of sufficiently large degree containing $Z$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-06T16:42:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14C20",
      "14C21",
      "14C22",
      "14C25",
      "14C30",
      "14F43",
      "14F45",
      "14J70"
    ],
    "keywords": [
      "base locus",
      "noether-lefschetz theory",
      "smooth complex projective variety",
      "intermediate neron-severi group",
      "general smooth hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.4528D"
    }
  }
}