{
  "id": "1601.07514",
  "version": "v1",
  "published": "2016-01-27T19:28:42.000Z",
  "updated": "2016-01-27T19:28:42.000Z",
  "title": "Hyperbolicity of cyclic covers and complements",
  "authors": [
    "Yuchen Liu"
  ],
  "comment": "16 pages; comments welcome",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We prove that a cyclic cover of a smooth complex projective variety is Brody hyperbolic if its branch divisor is a generic small deformation of a large enough multiple of a Brody hyperbolic base-point-free ample divisor. We also show the hyperbolicity of complements of those branch divisors. As an application, we find new examples of Brody hyperbolic hypersurfaces in $\\mathbb{P}^{n+1}$ that are cyclic covers of $\\mathbb{P}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-27T19:28:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic cover",
      "complements",
      "brody hyperbolic base-point-free ample divisor",
      "hyperbolicity",
      "branch divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160107514L"
    }
  }
}