Remarks on the existence of minimal models of log canonical generalized pairs

Abstract

Given an NQC log canonical generalized pair $(X,B+M)$ whose underlying variety $X$ is not necessarily $\mathbb{Q}$-factorial, we show that one may run a $(K_X+B+M)$-MMP with scaling of an ample divisor which terminates, provided that $(X,B+M)$ has a minimal model in a weaker sense or that $K_X+B+M$ is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance, when the boundary contains an ample divisor.

v3: minor changes, following the referee's comments; to appear in Math. Z

References in corpus (6)

• The Nonvanishing problem for varieties with nef anticanonical bundle
• Special MMP for log canonical generalised pairs
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• Special termination for log canonical pairs
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Cited by in corpus (2)

• Minimal model program for algebraically integrable foliations on klt varieties
• Minimal model program for normal pairs along log canonical locus