Hyperbolicity in Complex Geometry

Yum-Tong Siu

A chapter in The Legacy of Niels Henrik Abel, 2004, pp 543-566 from Springer

Abstract: Abstract A complex manifold is said to be hyperbolic if there exists no nonconstant holomorphic map from the affine complex line to it. We discuss the techniques and methods for the hyperbolicity problems for submanifolds and their complements in abelian varieties and the complex projective space. The discussion is focussed on Bloch’s techniques for the abelian variety setting, the recent confirmation of the longstanding conjecture of the hyperbolicity of generic hypersurfaces of high degree in the complex projective space, and McQuillan’s techniques for compact complex algebraic surfaces of general type.

Keywords: Line Bundle; Meromorphic Function; Abelian Variety; Complex Projective Space; Diophantine Approximation (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18908-1_16

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DOI: 10.1007/978-3-642-18908-1_16

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