MMPforFdlt
“Theorem A. Let (X, F, B) be a Q-factorial projective F-dlt foliated triple such that F is algebraically integrable. Let A be an ample R-divisor on X. Then: (1) The cone theorem, contraction theorem, and the existence of flips hold for (X, F, B). In particular, we can run a (KF + B)-MMP. (2) If KF + B + A is nef, then KF + B + A is semi-ample1. (3) If B ≥ A ≥ 0, then (X, F, B) has a good minimal model or a Mori fiber space. (4) If KF + B + A is Q-Cartier, then the canonical ring of KF + B + A, R(X, KF + B + A) = +∞ ⊕ m=0 H0(X, OX (⌊m(KF + B + A)⌋)), is finitely generated.” (Chen 等, 2023)