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

Abstract

AbstractGiven an NQC log canonical generalized pair $$(X,B+M)$$ ( X , B + M ) whose underlying variety X is not necessarily $$\mathbb {Q}$$ Q -factorial, we show that one may run a $$(K_X+B+M)$$ ( K X + B + M ) -MMP with scaling of an ample divisor which terminates, provided that $$(X,B+M)$$ ( X , B + M ) has a minimal model in a weaker sense or that $$K_X+B+M$$ 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.