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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The hyperbolicity of the complement of $ 2n+1$ hyperplanes in general position in $ P\sb{n}$ and related results


Author: Mark L. Green
Journal: Proc. Amer. Math. Soc. 66 (1977), 109-113
MSC: Primary 32H20
MathSciNet review: 0457790
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Abstract | References | Similar Articles | Additional Information

Abstract: Using a modified version of a technique of R. Brody, a simple proof is found that the complement of 2n + 1 hyperplanes in general position in $ {{\mathbf{P}}_n}$ is complete hyperbolic and hyperbolically embedded in $ {{\mathbf{P}}_n}$. In fact, a more general result is obtained showing that a suitable Picard theorem is sufficient to imply hyperbolicity in a large class of algebro-geometric situations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0457790-9
PII: S 0002-9939(1977)0457790-9
Keywords: Hyperbolic manifold, holomorphic curve, value distribution theory, Picard theorem, hyperplanes in general position, complex projective spaces
Article copyright: © Copyright 1977 American Mathematical Society