Hyperbolic hypersurfaces in P^n of Fermat-Waring type

Bernard Shiffman (1) , Mikhail Zaidenberg (2)

1 department of Mathematics
2 IF - Institut Fourier

In this note we show that there are algebraic families of hyperbolic, Fermat-Waring type hypersurfaces in P^n of degree 4(n-1)^2, for all dimensions n>1. Moreover, there are hyperbolic Fermat-Waring hypersurfaces in P^n of degree 4n^2-2n+1 possessing complete hyperbolic, hyperbolically embedded complements.

S 0002-9939(01)06417-6Article electronically published on December 27, 2001

Mots clés: projective hypersurface; Fermat-Waring hypersurface; hyperbolicity

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Bernard Shiffman, Mikhail Zaidenberg. Hyperbolic hypersurfaces in P^n of Fermat-Waring type. Proceedings of the American Mathematical Society, 2002, 130 (7), pp.2031-2035. ⟨10.1090/S0002-9939-01-06417-6⟩. ⟨hal-00323758⟩