A construction of hyperbolic hypersurface of \(P^ n(C)\). (English) Zbl 0844.32018

S. Kobayashi conjectured in 1970 that a generic hypersurface of large degree of the complex projective space \(\mathbb{P}^n (\mathbb{C})\) of dimension \(n\) is hyperbolic, and that its complement is hyperbolic and moreover hyperbolically embedded into \(\mathbb{P}^n (\mathbb{C})\). Even the existence of such hypersurfaces has been known only for \(n \leq 3\). In this paper we construct such hypersurfaces for all \(n \geq 2\).
Reviewer: K.Masuda (Tokyo)


32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
32F45 Invariant metrics and pseudodistances in several complex variables
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