Special MMP for log canonical generalised pairs (with an appendix joint with Xiaowei Jiang)

Abstract

We show that minimal models of mathbb {Q}-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a mathbb {Q}-factorial NQC log canonical generalised pair (X,B+M) we can run an MMP with scaling of an ample divisor which terminates, assuming that it admits an NQC weak Zariski decomposition or that K_X+B+M is not pseudoeffective. As a consequence, we establish several existence results for minimal models and Mori fibre spaces.