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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)

##### MSC:
 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 32F45 Invariant metrics and pseudodistances in several complex variables
##### Keywords:
hyperbolic hypersurface; complex projective space
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##### References:
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