Rank one foliations on toroidal varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918436736598016 |
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| author | Spicer, Calum Tasin, Luca |
| author_facet | Spicer, Calum Tasin, Luca |
| contents | Consider a log canonical pair $(X,B)$ such that there is a Cartier divisor $D$ for which $T_X(-\log B) \otimes \mathcal O(D)$ is locally free and globally generated. Let $\mathcal F$ be a log canonical foliation of rank 1 on $X$. We prove that there exists a divisor $Γ$ such that $(X, Γ)$ is log canonical and $K_X + Γ\sim K_{\mathcal F} + D$.
We then apply this result to prove several statements on the birational geometry of rank 1 log canonical foliations on log homogeneous varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rank one foliations on toroidal varieties Spicer, Calum Tasin, Luca Algebraic Geometry Complex Variables Consider a log canonical pair $(X,B)$ such that there is a Cartier divisor $D$ for which $T_X(-\log B) \otimes \mathcal O(D)$ is locally free and globally generated. Let $\mathcal F$ be a log canonical foliation of rank 1 on $X$. We prove that there exists a divisor $Γ$ such that $(X, Γ)$ is log canonical and $K_X + Γ\sim K_{\mathcal F} + D$. We then apply this result to prove several statements on the birational geometry of rank 1 log canonical foliations on log homogeneous varieties. |
| title | Rank one foliations on toroidal varieties |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2604.08100 |