Weak analytic hyperbolicity of complements of generic surfaces of high degree in projective 3-space. (English) Zbl 1140.32013

Rousseau, Erwan

Osaka J. Math. 44, No. 4, 955-971 (2007).

In this paper the author proves that every entire curve in the complement of a generic hypersurface of degree \(d\geq 586\) in \({\mathbb P}^3({\mathbb C})\) is contained in a proper subvariety. This is a weak form of the famous Kobayashi conjecture claiming the Kobayashi hyperbolicity of the complement of a generic hypersurface of degree \(d\geq 2n+1\) in \({\mathbb P}^n({\mathbb C})\). The proof of the main result of this paper is based on the construction of a sufficiently large number of logarithmic jet differentials on the complement of a generic hypersurface in \({\mathbb P}^3({\mathbb C})\).

Reviewer: Marco Abate (Pisa)

MSC:

32Q45	Hyperbolic and Kobayashi hyperbolic manifolds
14J70	Hypersurfaces and algebraic geometry

Keywords:

Kobayashi hyperbolicity; logarithmic jet budles

References:

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