Hyperbolicity and fundamental groups of complex quasi-projective varieties (I): Maximal quasi-Albanese dimension by Nevanlinna theory

2025/11/06 by Benoît Cadorel, Cadorel, Benoit, Ya Deng +3 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2511.04405

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

This is the first part of a series of three papers. In this paper, we establish a Big Picard type theorem for holomorphic maps f:Y → X, where Y is a ramified covering of the punctured disc \mathbbD^* with small ramification and X is a complex quasi-projective variety of log-general type and of maximal quasi-Albanese dimension. As a byproduct, we prove the generalized Green-Griffiths-Lang conjecture for such X. This paper summarizes the parts of the three-paper series that are based primarily on Nevanlinna theory.

Citations

• Entire curves in C-pairs with large irregularity
• Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials
• Hyperbolicity and fundamental groups of complex quasi-projective varieties
• Pluriharmonic maps into buildings and symmetric differentials
• Picard hyperbolicity of manifolds admitting nilpotent harmonic bundles
• Non-reductive geometric invariant theory and hyperbolicity
• Notes on the weak positivity theorems
• Logarithmic Jets and Hyperbolicity
• On the abc conjecture and diophantine approximation by rational points
• Characterization of Abelian Varieties

Cited by

• Hyperbolicity and fundamental groups of complex quasi-projective varieties (III): applications
• Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories

Related

• Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories
• Hyperbolicity and fundamental groups of complex quasi-projective varieties
• Hyperbolicity and fundamental groups of complex quasi-projective varieties (III): applications
• The relative Green-Griffiths-Lang conjecture for families of varieties of maximal Albanese dimension
• Big Picard theorem for moduli spaces of polarized manifolds