The algebraic Green-Griffiths-Lang conjecture for complements of very general pairs of divisors

2024/10/01 by Ascher, Kenneth, Turchet, Amos, Yeong, Wern · 2 citations
#14C20 #14J70 #32Q45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.00640

Abstract

We prove that the complement of a very general pair of hypersurfaces of total degree 2n in ℙⁿ is algebraically hyperbolic modulo a proper closed subvariety. This provides evidence towards conjectures of Lang-Vojta and Green-Griffiths, and partially extends previous work of Chen, Pacienza-Rousseau, and Chen-Riedl and the third author.

Cited by

• Log algebraic hyperbolicity of M_0,n
• Algebraic Exceptional Set of a Three-Component Curve on Hirzebruch Surfaces

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