{
  "id": "0904.2445",
  "version": "v1",
  "published": "2009-04-16T08:28:17.000Z",
  "updated": "2009-04-16T08:28:17.000Z",
  "title": "Positive sheaves of differentials coming from coarse moduli spaces",
  "authors": [
    "Kelly Jabbusch",
    "Stefan Kebekus"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base U, and suppose the family is non-isotrivial. If Y is a smooth compactification of U, such that D := Y U is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along D. Viehweg and Zuo have shown that for some number m>0, the m-th symmetric power of this sheaf admits many sections. More precisely, the m-th symmetric power contains an invertible sheaf whose Kodaira-Iitaka dimension is at least the variation of the family. We refine this result and show that this \"Viehweg-Zuo sheaf\" comes from the coarse moduli space associated to the given family, at least generically. As an immediate corollary, if U is a surface, we see that the non-isotriviality assumption implies that U cannot be special in the sense of Campana.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-16T08:28:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D22"
    ],
    "keywords": [
      "coarse moduli space",
      "positive sheaves",
      "differentials coming",
      "m-th symmetric power contains",
      "simple normal crossing divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2445J"
    }
  }
}