# On the hyperbolicity of general hypersurfaces

@article{Brotbek2016OnTH, title={On the hyperbolicity of general hypersurfaces}, author={Damian Brotbek}, journal={Publications math{\'e}matiques de l'IH{\'E}S}, year={2016}, volume={126}, pages={1-34} }

In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in Pn$\mathbf {P}^{n}$ are hyperbolic. In this paper we prove that a general sufficiently ample hypersurface in a smooth projective variety is hyperbolic. To prove this statement, we construct hypersurfaces satisfying a property which is Zariski open and which implies hyperbolicity. These hypersurfaces are chosen such that the geometry of their higher order jet spaces can be related to the geometry of a…

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