Algebraic Hyperbolicity of Complements of Generic Hypersurfaces in Projective Spaces

2022/08/15 by Xi Chen, Chen, Xi, Eric Riedl +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2208.07401

openalex publication_date 2022/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the algebraic hyperbolicity of the complement of very general degree 2n hypersurfaces in Pⁿ. 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.

Cited by

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

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