Existence of minimal models for threefold generalized pairs in positive characteristic

Abstract

Let $\mathbb{K}$ be an algebraically closed field of characteristic $p>5$. We show the existence of minimal models for pseudo-effective NQC lc generalized pairs in dimension three over $\mathbb{K}$. As a consequence, we prove the termination of flips for pseudo-effective threefold NQC lc generalized pairs over $\mathbb{K}$. This provides a new proof on the termination of flips for pseudo-effective pairs over $\mathbb{K}$ without using the non-vanishing theorems. A key ingredient of our proof is the ACC for lc thresholds in dimension $\leq 3$ and the global ACC in dimension $\leq 2$ for generalized pairs over $\mathbb{K}$.