Abstract.
In this paper we prove a conjectured height inequality of Lang and Vojta for holomorphic curves lying on generic hyperplane sections of 3-folds. As a consequence we deduce a conjecture of Kobayashi that a generic hypersurface in \( {\Bbb P}^3_{\Bbb C} \) of sufficiently high degree is hyperbolic.
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Submitted: June 1998.
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McQuillan, M. Holomorphic Curves on Hyperplane Sections of 3-Folds. GAFA, Geom. funct. anal. 9, 370–392 (1999). https://doi.org/10.1007/s000390050091
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DOI: https://doi.org/10.1007/s000390050091