{
  "id": "1908.08573",
  "version": "v1",
  "published": "2019-08-22T19:29:24.000Z",
  "updated": "2019-08-22T19:29:24.000Z",
  "title": "Kobayashi non-hyperbolicity of Calabi-Yau manifolds via mirror symmetry",
  "authors": [
    "Ljudmila Kamenova",
    "Cumrun Vafa"
  ],
  "comment": "8 pages, comments are welcome",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "A compact complex manifold is Kobayashi non-hyperbolic if there exists an entire curve on it. Using mirror symmetry we establish that there are (possibly singular) elliptic or rational curves on any Calabi-Yau manifold $X$, whose mirror dual $\\check X$ exists and is not \"Hodge degenerate\", therefore proving that $X$ is Kobayashi non-hyperbolic. We are not aware of any higher dimensional simply connected Calabi-Yau manifolds that satisfy the \"Hodge degenerate\" condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T19:29:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mirror symmetry",
      "kobayashi non-hyperbolicity",
      "hodge degenerate",
      "higher dimensional simply connected calabi-yau",
      "compact complex manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}