Rank one foliations on toroidal varieties
Calum Spicer, Luca Tasin

TL;DR
This paper studies rank one foliations on toroidal varieties, establishing a relation between their canonical divisors and log canonical pairs, with applications to birational geometry.
Contribution
It proves the existence of a divisor relating the canonical class of the foliation to a log canonical pair, advancing understanding of foliations on toroidal varieties.
Findings
Existence of a divisor $Gamma$ such that $(X, Gamma)$ is log canonical and relates to the foliation's canonical class.
Application of the main result to birational geometry of rank 1 log canonical foliations.
Insights into the structure of foliations on log homogeneous varieties.
Abstract
Consider a log canonical pair such that there is a Cartier divisor for which is locally free and globally generated. Let be a log canonical foliation of rank 1 on . We prove that there exists a divisor such that is log canonical and . 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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