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

摘要

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 Alexecv-Borisov conjecture in dimension 3.