{
  "id": "2307.03938",
  "version": "v1",
  "published": "2023-07-08T09:13:55.000Z",
  "updated": "2023-07-08T09:13:55.000Z",
  "title": "Abundance for threefolds in positive characteristic when $ν=2$",
  "authors": [
    "Zheng Xu"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we prove the abundance conjecture for threefolds over an algebraically closed field $k$ of characteristic $p > 3$ in the case of numerical dimension equals to $2$. More precisely, we prove that if $(X,B)$ be a projective lc threefold pair over $k$ such that $K_{X}+B$ is nef and $\\nu(K_{X}+B)=2$, then $K_{X}+B$ is semiample.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-08T09:13:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive characteristic",
      "projective lc threefold pair",
      "abundance conjecture",
      "numerical dimension equals",
      "algebraically closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}