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arXiv · 2609.15628

Algebraic hyperbolicity of very general hypersurfaces in projective spaces

Sixuan Lou·Junyan Zhao
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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.

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Sixuan Lou, Junyan Zhao. 2026-09-16. Algebraic hyperbolicity of very general hypersurfaces in projective spaces. https://arxiv.org/abs/2609.15628

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