{
  "id": "1612.06520",
  "version": "v1",
  "published": "2016-12-20T06:26:19.000Z",
  "updated": "2016-12-20T06:26:19.000Z",
  "title": "On the projective normality of cyclic coverings over a rational surface",
  "authors": [
    "Lei Song"
  ],
  "comment": "comments welcome",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let $S$ be a rational surface with $\\dim|-K_S|\\ge 1$ and let $\\pi: X\\rightarrow S$ be a ramified cyclic covering from a smooth surface $X$ with the Kodaira dimension $\\kappa(X)\\ge 0$. We prove that for any integer $k\\ge 3$ and ample divisor $A$ on $S$, the adjoint divisor $K_X+k\\pi^*A$ is very ample and normally generated. Similar result holds for minimal (possibly singular) coverings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-20T06:26:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational surface",
      "cyclic covering",
      "projective normality",
      "similar result holds",
      "kodaira dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}