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arXiv · 2603.03817

Existence of the minimal model program for log canonical generalized pairs

Zhengyu Hu·Jihao Liu
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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 Koll\'ar-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.

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Zhengyu Hu, Jihao Liu. 2026-03-04. Existence of the minimal model program for log canonical generalized pairs. https://arxiv.org/abs/2603.03817

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