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arXiv · 2406.19003

Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials

Benoit Cadorel
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Abstract

We give a new version of a recent result of B{\'e}rczi-Kirwan, proving the Kobayashi and Green-Griffiths-Lang conjectures for generic hypersurfaces in the projective space , with a polynomial lower bound on the degree. Our strategy again relies on Siu's technique of slanted vector fields and the use of holomorphic Morse inequalities to prove the existence of a jet differential equation with a negative twist -- however, instead of using a space of invariant jet differentials, we base our computations on the classical Green-Griffiths jet spaces.

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Benoit Cadorel. 2024-06-27. Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials. https://arxiv.org/abs/2406.19003

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