Algebraic Hyperbolicity of Complements of Generic Hypersurfaces in Projective Spaces

TL;DR

This paper proves the algebraic hyperbolicity of complements of very general degree 2n hypersurfaces in projective spaces, confirming the Green-Griffiths-Lang Conjecture for these cases and characterizing exceptional loci for specific instances.

Contribution

It establishes the algebraic hyperbolicity of these complements and verifies the Green-Griffiths-Lang Conjecture in this context, providing a complete description for quartic plane curves.

Findings

Proves algebraic hyperbolicity for complements of degree 2n hypersurfaces in P^n.

Confirms the Green-Griffiths-Lang Conjecture for these complements.

Characterizes the exceptional locus for quartic plane curve complements.

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.