{
  "id": "1410.5868",
  "version": "v1",
  "published": "2014-10-21T22:04:29.000Z",
  "updated": "2014-10-21T22:04:29.000Z",
  "title": "The primitive cohomology of theta divisors",
  "authors": [
    "E. Izadi",
    "J. Wang"
  ],
  "comment": "To appear in the proceedings of the conference on Hodge Theory and Classical Algebraic Geometry at the Ohio State University, May 2013",
  "categories": [
    "math.AG"
  ],
  "abstract": "The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension $g$ is a Hodge structure of level $g-3$. The Hodge conjecture predicts that it is contained in the image, under the Abel-Jacobi map, of the cohomology of a family of curves in the theta divisor. We survey some of the results known about this primitive cohomology, prove a few general facts and mention some interesting open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-21T22:04:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C30",
      "14K99"
    ],
    "keywords": [
      "theta divisor",
      "primitive cohomology",
      "hodge conjecture predicts",
      "principally polarized abelian variety",
      "hodge structure"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5868I"
    }
  }
}