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

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arxiv 2410.00640 v1 pith:C62H652N submitted 2024-10-01 math.AG math.NT

Kenneth Ascher , Amos Turchet , Wern Yeong This is my paper · ORCID
classification math.AGmath.NT
keywords generalveryalgebraicalgebraicallyauthorchenchen-riedlclosed
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abstract

We prove that the complement of a very general pair of hypersurfaces of total degree $2n$ in $\mathbb{P}^n$ 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Pseudo-hyperbolicity of Horikawa surfaces

    math.AG 2026-08 conditional novelty 7.0 of 10

    Very general Horikawa surfaces with p_g ≥ 5 (and first-kind with p_g = 3, 4) contain only finitely many rational or elliptic curves, with explicit counts in most strata.

  2. Algebraic Exceptional Set of a Three-Component Curve on Hirzebruch Surfaces

    math.AG 2025-07 conditional novelty 6.0 of 10

    For Hirzebruch surfaces, the algebraic exceptional set of a three-component normal-crossing curve with big K+B and no fiber or negative self-intersection component is finite and equals the hyper-bitangent set.

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