{
  "id": "2103.02180",
  "version": "v1",
  "published": "2021-03-03T04:58:08.000Z",
  "updated": "2021-03-03T04:58:08.000Z",
  "title": "Bounded negativity and bounding cohomology on a smooth projective surface with Picard number two",
  "authors": [
    "Sichen Li"
  ],
  "comment": "6 pages, Comments are welcome. arXiv admin note: text overlap with arXiv:2007.12855",
  "categories": [
    "math.AG"
  ],
  "abstract": "A conjecture of the bounding cohomology on a smooth projective surface $X$ asserts that there exists a positive constant $c_X$ such that $h^1(\\mathcal O_X(C))\\le c_Xh^0(\\mathcal O_X(C))$ for every prime divisor $C$ on $X$. When the Picard number $\\rho(X)=2$, we prove that if the Kodaira dimension $\\kappa(X)=-\\infty$ and $X$ has a negative curve, then this conjecture holds for $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-03T04:58:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20"
    ],
    "keywords": [
      "smooth projective surface",
      "picard number",
      "bounding cohomology",
      "bounded negativity",
      "conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}