{
  "id": "1305.6024",
  "version": "v1",
  "published": "2013-05-26T14:07:31.000Z",
  "updated": "2013-05-26T14:07:31.000Z",
  "title": "The subadditivity of the Kodaira Dimension for Fibrations of Relative Dimension One in Positive Characteristics",
  "authors": [
    "Yifei Chen",
    "Lei Zhang"
  ],
  "comment": "14 pages, welcome comments",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $f:X\\rightarrow Z$ be a separable fibration of relative dimension 1 between smooth projective varieties over an algebraically closed field $k$ of positive characteristic. We prove the subadditivity of Kodaira dimension $\\kappa(X)\\geq\\kappa(Z)+\\kappa(F)$, where $F$ is the generic geometric fiber of $f$, and $\\kappa(F)$ is the Kodaira dimension of the normalization of $F$. Moreover, if $\\dim X=2$ and $\\dim Z=1$, we have a stronger inequality $\\kappa(X)\\geq \\kappa(Z)+\\kappa_1(F)$ where $\\kappa_1(F)=\\kappa(F,\\omega^o_F)$ is the Kodaira dimension of the dualizing sheaf $\\omega_F^o$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-26T14:07:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kodaira dimension",
      "relative dimension",
      "positive characteristic",
      "subadditivity",
      "generic geometric fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6024C"
    }
  }
}