Boundedness in general type MMP
arXiv:2506.20183
Abstract
We show that in any sequence of a general type MMP, the minimal log discrepancy of singularities takes at most finitely many values, and the fibers of all the extremal contractions and flips belong to a bounded family. A key ingredient in the proof is an analysis of the behavior of local volumes in the MMP.
45 pages. First part of a two-paper replacement of the original submission. Comments are welcome!