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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyperbolic surfaces in ${\mathbb P}^3(\mathbb C)$
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by Ha Huy Khoai PDF
Proc. Amer. Math. Soc. 125 (1997), 3527-3532 Request permission

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
  • Received by editor(s): March 16, 1995
  • Communicated by: Eric Bedford
  • © Copyright 1997 American Mathematical Society
  • 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