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Algebraic Hyperbolicity of Complements of Generic Hypersurfaces in Projective Spaces

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arxiv 2208.07401 v2 pith:OICDFOKF submitted 2022-08-15 math.AG math.NT

Xi Chen , Eric Riedl , Wern Yeong This is my paper · ORCID
classification math.AGmath.NT
keywords algebraiccomplementcomplementshyperbolicityhypersurfacesbitangentcasecharacterize
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abstract

We study the algebraic hyperbolicity of the complement of very general degree $2n$ hypersurfaces in P^n. We prove the Algebraic Green-Griffiths-Lang Conjecture for these complements, and in the case of the complement of a quartic plane curve, we completely characterize the exceptional locus as the union of the flex and bitangent lines.

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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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