, Volume 9, Issue 2, pp 370-392

Holomorphic Curves on Hyperplane Sections of 3-Folds

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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.

Submitted: June 1998.