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.