Holomorphic Curves on Hyperplane Sections of 3-Folds

摘要

In this paper we prove a conjectured height inequality of Lang and Vojta forholomorphic curves lying on generic hyperplane sections of a 3-fold with Neron-Severi group of rank 1. As a consequence we deduce a conjecture of Kobayashi that a generic hypersurface in P3C of sufficiently high degree is hyperbolic.