We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a \({\mathbb {Q}}\)-factorial projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial foliated pairs.

中文翻译：

---

MMP用于将一叶分为三级

我们证明了翻转，特殊终止，无基点定理的存在，并且在对数一般类型的情况下，证明了\（{\ mathbb {Q} } \）-因子射影的三倍。作为应用，我们显示了叶对存在F-dlt修饰和F末端，并且我们显示具有规范或F-dlt奇异性的叶面允许非二元奇异性。最后，在数值上琐碎的叶对的情况下，我们显示出丰富的内容。