Hyperbolic hypersurfaces in ℙⁿ of Fermat-Waring type

Shiffman, Bernard; Zaidenberg, Mikhail

doi:10.1090/S0002-9939-01-06417-6

Hyperbolic hypersurfaces in $\mathbb P^n$ of Fermat-Waring type
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Proc. Amer. Math. Soc. 130 (2002), 2031-2035 Request permission

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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