Geometric & Functional Analysis GAFA

, Volume 9, Issue 2, pp 370–392

Holomorphic Curves on Hyperplane Sections of 3-Folds

  • M. McQuillan

DOI: 10.1007/s000390050091

Cite this article as:
McQuillan, M. GAFA, Geom. funct. anal. (1999) 9: 370. doi:10.1007/s000390050091


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.

Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • M. McQuillan
    • 1
  1. 1.All Souls College, Oxford, 0X1 4AL, United KingdomGB

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