Hyperbolicity of Nodal Hypersurfaces

@inproceedings{Bogomolov2005HyperbolicityON,
  title={Hyperbolicity of Nodal Hypersurfaces},
  author={Fedor Bogomolov and Bruno Trevizan de Oliveira},
  year={2005}
}
We show that a nodal hypersurface X in P3 of degree d with a sufficiently large number l of nodes, l > 8 3 (d2 − 5 2 d), is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families. 

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