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

Abstract

AbstractWe show that minimal models of$$\mathbb {Q}$$Q-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a$$\mathbb {Q}$$Q-factorial NQC log canonical generalised pair$$ (X,B+M) $$(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$$ K_X+B+M$$KX+B+Mis not pseudoeffective. As a consequence, we establish several existence results for minimal models and Mori fibre spaces.