Optimal bend-and-break for foliations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866916034972221440 |
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| author | Liu, Jihao Sun, Zeming Jiang, Jiedong |
| author_facet | Liu, Jihao Sun, Zeming Jiang, Jiedong |
| contents | We show that for every foliation $\mathcal{F}$ of rank $r$ on a normal projective variety, the optimal constant in the bend-and-break inequality for tangent rational curves is $r+1$. The proof combines the method of Bogomolov--McQuillan and the bend-and-shatter method developed by Jovinelly--Lehmann--Riedl. The proof of the main result of this paper substantially uses generative AI, particularly the Rethlas system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal bend-and-break for foliations Liu, Jihao Sun, Zeming Jiang, Jiedong Algebraic Geometry 14J32 We show that for every foliation $\mathcal{F}$ of rank $r$ on a normal projective variety, the optimal constant in the bend-and-break inequality for tangent rational curves is $r+1$. The proof combines the method of Bogomolov--McQuillan and the bend-and-shatter method developed by Jovinelly--Lehmann--Riedl. The proof of the main result of this paper substantially uses generative AI, particularly the Rethlas system. |
| title | Optimal bend-and-break for foliations |
| topic | Algebraic Geometry 14J32 |
| url | https://arxiv.org/abs/2605.20754 |