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Hyperbolic surfaces in $\mathbb P^3(\mathbb C)$


Author: Ha Huy Khoai
Journal: Proc. Amer. Math. Soc. 125 (1997), 3527-3532
MSC (1991): Primary 32H20
DOI: https://doi.org/10.1090/S0002-9939-97-04200-7
MathSciNet review: 1443160
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Abstract: We show a class of perturbations $X$ of the Fermat hypersurface such that any holomorphic curve from $\mathbb C$ into $X$ is degenerate. Applying this result, we give explicit examples of hyperbolic surfaces in $\mathbb P^3(\mathbb C)$ of arbitrary degree $d\ge 22$, and of curves of arbitrary degree $d\ge 19$ in $\mathbb P^2(\mathbb C)$ with hyperbolic complements.


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Additional Information

Ha Huy Khoai
Affiliation: Institute of Mathematics, P.O. Box 631, Bo Ho, 10000 Hanoi, Vietnam
Email: hhkhoai@thevinh.ac.vn

DOI: https://doi.org/10.1090/S0002-9939-97-04200-7
Keywords: Holomorphic curves, hyperbolic surfaces
Received by editor(s): March 16, 1995
Communicated by: Eric Bedford
Article copyright: © Copyright 1997 American Mathematical Society

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