Work

Algebraic hyperbolicity of very general hypersurfaces in projective spaces

Year: 2026

Type: preprint

Abstract: We prove that a very general sextic threefold in $\mathbb{P}^4$ is algebraically hyperbolic, settling the last open case and completing the classification of algebraic hyperbolicity for very general hypersurfaces in projective space. The proof follows the Coskun--Riedl scroll construction, with the moduli of stable maps and the geometric canonical height as new ingredients.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.15628

Authors: Lou, Sixuan, Zhao, Junyan

Institutions: University of Illinois Chicago, University of Maryland, College Park

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213350990

Cites: 1

Cited by:

Related to: 10