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

Abstract

We show that minimal models of Q-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a 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 KX + B + M is not pseudoeffective. As a consequence, we establish several existence results for minimal models and Mori fibre spaces.