Weak analytic hyperbolicity of complements of generic surfaces of high degree in projective 3-space

2006/03/30 by Erwan Rousseau, Rousseau, Erwan · 1 citation
Mathematics · #14J70 #32Q45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0603715

openalex publication_date 2006/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove that every entire curve in the complement of a generic hypersurface of degree d≥ 586 in ℙ_ℂ³ is algebraically degenerate i.e there exists a proper subvariety which contains the entire curve.

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• A Second Main Theorem for Entire Curves Intersecting Three Conics

Related

• Weak analytic hyperbolicity of generic hypersurfaces of high degree in the complex projective space of dimension 4
• Effective algebraic degeneracy of entire curves in complements of smooth projective hypersurfaces
• Algebraic Hyperbolicity of Complements of Generic Hypersurfaces in Projective Spaces
• Algebraic hyperbolicity of the very general quintic surface in ℙ³
• Nondeformability of entire curves in projective hypersurfaces of high degree