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 w...
Ausführliche Beschreibung

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. Ausführliche Beschreibung