Degeneracy of Holomorphic Curves into Algebraic Varieties

2005/07/06 by Junjiro Noguchi, Noguchi, Junjiro, Jörg Winkelmann +3 · 3 citations
Mathematics · #32H30 #32Q45 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:32H30 #msc:32Q45

paper · pdf · doi:10.48550/arxiv.math/0507122

LaTeX, 22 pages

arxiv created 2005/07/06 · arxiv updated 2009/12/01

Abstract

Applying the Second Main Theorem we deal with the algebraic degeneracy of entire holomorphic curves from the complex plane into a complex algebraic normal variety of positive log Kodaira dimension that admits a finite proper morphism to a semi-abelian variety. We will also discuss applications to the Kobayashi hyperbolicity problem.

Cited by

• A Second Main Theorem for Entire Curves Intersecting Three Conics
• Hyperbolicity and GCD for n+1 divisors with non-empty intersection
• Campana's orbifold conjecture for numerically equivalent divisors

Related

• Algebraic degeneracy of holomorphic curves
• On Holomorphic Curves in Semi-Abelian Varieties
• Recent results on the Kobayashi and Green-Griffiths-Lang conjectures
• Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces
• Bloch's principle for holomorphic maps into subvarieties of semi-abelian varieties