{
  "id": "0711.0964",
  "version": "v2",
  "published": "2007-11-06T20:42:35.000Z",
  "updated": "2008-02-18T23:18:47.000Z",
  "title": "Singularities of admissible normal functions",
  "authors": [
    "Patrick Brosnan",
    "Hao Fang",
    "Zhaohu Nie",
    "Gregory Pearlstein"
  ],
  "comment": "23 pages. Added section describing the behavior of singularities under blowing up. This connects our work directly with that of Green and Griffiths",
  "categories": [
    "math.AG"
  ],
  "abstract": "In a recent paper, M. Green and P. Griffiths used R. Thomas' works on nodal hypersurfaces to establish the equivalence of the Hodge conjecture and the existence of certain singular admissible normal functions. Inspired by their work, we study normal functions using M. Saito's mixed Hodge modules and prove that the existence of singularities of the type considered by Griffiths and Green is equivalent to the Hodge conjecture. Several of the intermediate results, including a relative version of the weak Lefschetz theorem for perverse sheaves, are of independent interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-18T23:18:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D07",
      "32S35"
    ],
    "keywords": [
      "singularities",
      "hodge conjecture",
      "saitos mixed hodge modules",
      "singular admissible normal functions",
      "study normal functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.0964B"
    }
  }
}