{
  "id": "1801.00739",
  "version": "v1",
  "published": "2018-01-02T17:39:08.000Z",
  "updated": "2018-01-02T17:39:08.000Z",
  "title": "Log canonical pairs over varieties with maximal Albanese dimension",
  "authors": [
    "Zhengyu Hu"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $(X,B)$ be a log canonical pair over a normal variety $Z$ with maximal Albanese dimension. If $K_X+B$ is relatively abundant over $Z$ (for example, $K_X+B$ is relatively big over $Z$), then we prove that $K_X+B$ is abundant. In particular, the subadditvity of Kodaira dimensions $\\kappa(K_X+B) \\geq \\kappa(K_F+B_F)+ \\kappa(Z)$ holds, where $F$ is a general fiber, $K_F+B_F= (K_X+B)|_F$, and $\\kappa(Z)$ means the Kodaira dimension of a smooth model of $Z$. We discuss several variants of this result in Section 4. We also give a remark on the log Iitaka conjecture for log canonical pairs in Section 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-02T17:39:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "log canonical pair",
      "maximal albanese dimension",
      "kodaira dimension",
      "log iitaka conjecture",
      "general fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}