Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909305576357888 |
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| author | Cadorel, Benoit |
| author_facet | Cadorel, Benoit |
| contents | We give a new version of a recent result of B{é}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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials Cadorel, Benoit Algebraic Geometry We give a new version of a recent result of B{é}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. |
| title | Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.19003 |