Ascending chain condition for log canonical thresholds and termination of log flips

Abstract

We prove that the ascending chain condition (ACC) for log canonical (lc) thresholds in dimension $d$, existence of log flips in dimension $d$, and the log minimal model program (LMMP) in dimension $d-1$ imply termination of any sequence of log flips starting with a $d$-dimensional effective lc pair and also imply termination of flops in dimension $d$. In particular, the latter terminations in dimension $4$ follow from the Alexeev-Borisov conjecture in dimension $3$