Log Canonical Minimal Model Program for corank one foliations on Threefolds (2410.05178v2)

Abstract: If $\mathcal{F}$ is a corank one foliation on a $\mathbb{Q}$-factorial normal projective threefold and $\Delta \geq 0$ a $\mathbb{Q}$-divisor on $X$ such that $(\mathcal{F}, \Delta)$ is foliated log canonical and $(X, \Delta)$ is klt, we show that $K_{\mathcal{F}} +\Delta$ admits a minimal model or a Mori fiber space. In case $(\mathcal{F}, \Delta)$ is boundary polarized and $K_{\mathcal{F}}+ \Delta$ is pseudoeffective, the minimal model is good. We also apply our results to study the relation between different minimal models, namely, any two minimal models of a given foliated log canonical pair can be connected by a sequence of flops and in the boundary polarized case, the minimal models are only finitely many in number.