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Hyperbolic hypersurfaces in $\mathbb P^n$ of Fermat-Waring type

Authors: Bernard Shiffman and Mikhail Zaidenberg
Journal: Proc. Amer. Math. Soc. 130 (2002), 2031-2035
MSC (2000): Primary 32Q45, 32H25; Secondary 14J70
Published electronically: December 27, 2001
MathSciNet review: 1896038
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Abstract: In this note we show that there are algebraic families of hyperbolic, Fermat-Waring type hypersurfaces in $\mathbb P^n$ of degree $4(n-1)^2$, for all dimensions $n\ge 2$. Moreover, there are hyperbolic Fermat-Waring hypersurfaces in $\mathbb P^n$ of degree $4n^2-2n+1$ possessing complete hyperbolic, hyperbolically embedded complements.

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Additional Information

Bernard Shiffman
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218

Mikhail Zaidenberg
Affiliation: Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, BP 74, 38402 St. Martin d’Hères cédex, France

Received by editor(s): January 26, 2001
Published electronically: December 27, 2001
Additional Notes: Research of the first author partially supported by NSF grant #DMS-9800479.
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society