Existence of the minimal model program for log canonical generalized pairs

Abstract

We introduce linearly decomposable (LD) generalized pairs, which serve as a workable substitute for rational decompositions in the non-NQC setting. Using LD generalized pairs, together with a refinement of special termination and Kollár-type gluing theory, we prove the existence of flips for log canonical generalized pairs without assuming the klt condition, the NQC condition, or $\mathbb{Q}$-factoriality. Together with the cone and contraction theorems, this yields the existence of the minimal model program for arbitrary log canonical generalized pairs.

arXiv comment55 pages, 1 figure