{
  "id": "1906.11451",
  "version": "v1",
  "published": "2019-06-27T06:28:42.000Z",
  "updated": "2019-06-27T06:28:42.000Z",
  "title": "Some non-vanishing results on log canonical pairs of dimension 4",
  "authors": [
    "Fanjun Meng"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $(X,\\Delta)$ be a log canonical pair over $\\mathbb{C}$ with $X$ a normal projective variety, $\\Delta$ an effective $\\mathbb{Q}$-divisor, and $K_X+\\Delta$ nef. We give a non-vanishing criterion for $K_X+\\Delta$ in dimension $n$ with $X$ uniruled, assuming various conjectures of LMMP in dimensions (up to) $n-1$ or $n$, and a semi-ampleness criterion in the irregular case. In particular, we obtain that if $X$ is a uniruled $4$-fold, then $\\kappa(K_X+\\Delta)\\geq 0$ and if $X$ is a $4$-fold with $q(X)>0$, then $K_X+\\Delta$ is semi-ample.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-27T06:28:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "log canonical pair",
      "non-vanishing results",
      "normal projective variety",
      "semi-ampleness criterion",
      "irregular case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}