Degree-one foliations on complete intersections
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909939333595136 |
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| author | Figueira, Mateus Kuster, Crislaine Lizarbe, Ruben Muniz, Alan |
| author_facet | Figueira, Mateus Kuster, Crislaine Lizarbe, Ruben Muniz, Alan |
| contents | We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for any smooth hypersurface of dimension at least three that is not a quadric threefold. The proof of these results follows essentially from a more general structure theorem for foliations on manifolds covered by lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degree-one foliations on complete intersections Figueira, Mateus Kuster, Crislaine Lizarbe, Ruben Muniz, Alan Algebraic Geometry Complex Variables We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for any smooth hypersurface of dimension at least three that is not a quadric threefold. The proof of these results follows essentially from a more general structure theorem for foliations on manifolds covered by lines. |
| title | Degree-one foliations on complete intersections |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2507.08090 |