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arXiv · 2604.08100

Rank one foliations on toroidal varieties

Calum Spicer·Luca Tasin
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Abstract

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 $\Gamma$ such that $(X, \Gamma)$ is log canonical and $K_X + \Gamma \sim K_{\mathcal F} + D$. We then apply this result to prove several statements on the birational geometry of rank 1 log canonical foliations on log homogeneous varieties.

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Calum Spicer, Luca Tasin. 2026-04-09. Rank one foliations on toroidal varieties. https://arxiv.org/abs/2604.08100

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