{
  "id": "1501.07625",
  "version": "v1",
  "published": "2015-01-28T08:47:35.000Z",
  "updated": "2015-01-28T08:47:35.000Z",
  "title": "Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces",
  "authors": [
    "Jean-Pierre Demailly"
  ],
  "comment": "This paper supersedes submission hal-01092537 / arXiv:1412.2986",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "The Green-Griffiths-Lang conjecture stipulates that for every projective variety $X$ of general type over ${\\mathbb C}$, there exists a proper algebraic subvariety of $X$ containing all non constant entire curves $f:{\\mathbb C}\\to X$. Using the formalism of directed varieties, we prove here that this assertion holds true in case $X$ satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle $T\\_X$. We then use this fact to confirm a long-standing conjecture of Kobayashi (1970), according to which a very general algebraic hypersurface of dimension $n$ and degree at least $2n+2$ in the complex projective space ${\\mathbb P}^{n+1}$ is hyperbolic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-28T08:47:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general hypersurfaces",
      "kobayashi conjecture",
      "hyperbolicity",
      "strong general type condition",
      "non constant entire curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150107625D"
    }
  }
}