Weak analytic hyperbolicity of generic hypersurfaces of high degree in the complex projective space of dimension 4

TL;DR

This paper proves that for generic hypersurfaces in complex projective 4-space with degree at least 593, all entire curves are contained in proper subvarieties, indicating a form of hyperbolicity.

Contribution

It establishes a new degree threshold for hyperbolicity of generic hypersurfaces in complex projective 4-space, advancing understanding of entire curves in complex geometry.

Findings

Entire curves in generic hypersurfaces of degree ≥ 593 are algebraically degenerated.

Provides a new lower bound for hyperbolicity in dimension 4.

Enhances knowledge of the distribution of entire curves in high-degree hypersurfaces.

Abstract

The main goal of this work is to prove that every entire curve in a generic hypersurface of degree greater than or equal to 593 in the complex projective space of dimension 4 is algebraically degenerated i.e contained in a proper subvariety.