{
  "id": "1909.08757",
  "version": "v1",
  "published": "2019-09-19T01:09:58.000Z",
  "updated": "2019-09-19T01:09:58.000Z",
  "title": "Asymptotic growth of global sections on open varieties",
  "authors": [
    "Gabriele Di Cerbo"
  ],
  "comment": "11 pages. Comments are welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a projective variety and let $E$ be a reduced divisor. We study the asymptotic growth of the dimension of the space of global sections of powers of a divisor $D$ on $X\\backslash E$. We show that it is always bounded by a polynomial of degree $\\dim(X)$, if finite. Furthermore, when $D$ is big, we characterize the finiteness of the cohomology groups in question. This answers a question of Zariski and Koll\\'ar.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-19T01:09:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global sections",
      "asymptotic growth",
      "open varieties",
      "cohomology groups",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}