Hyperbolicity and GCD for n+1 divisors with non-empty intersection

2025/06/04 by Wang, Julie Tzu-Yueh, Xiao, Zheng
#Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.03534

Abstract

We study hyperbolicity for quasi-projective varieties where the boundary divisor consists of n+1 numerically parallel effective divisors on a complex projective variety of dimension n, allowing non-empty intersection. Under explicit local conditions on beta constants or intersection multiplicities, we prove that all entire curves are algebraically degenerate. Our approach extends the method of Levin-Huang-Xiao to higher dimensions, establishing a second main theorem for regular sequences of closed subschemes. This also yields a GCD-type estimate in the same geometric setting.

Citations

• Campana's orbifold conjecture for numerically equivalent divisors
• A New Diophantine Approximation Inequality on Surfaces and Its Applications
• Greatest Common Divisors on the Complement of Numerically Parallel Divisors
• Vojta's abc Conjecture for algebraic tori and applications over function fields
• The Ru-Vojta result for subvarieties
• Birational Nevanlinna constants, beta constants, and diophantine approximation to closed subschemes
• Greatest common divisors of analytic functions and Nevanlinna theory on\n algebraic tori
• A birational Nevanlinna constant and its consequences
• Degeneracy of Holomorphic Curves into Algebraic Varieties

Related

• Divisibility of polynomials and degeneracy of integral points
• About the hyperbolicity of complete intersections
• Degeneracy of Holomorphic Curves into Algebraic Varieties
• Some Remarks on Generic Complete Intersection Varieties
• On the degeneracy of integral points and entire curves in the complement of nef effective divisors