English

Boundedness in general type MMP

Algebraic Geometry 2025-09-03 v2

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.

Keywords

Cite

@article{arxiv.2506.20183,
  title  = {Boundedness in general type MMP},
  author = {Jingjun Han and Lu Qi and Ziquan Zhuang},
  journal= {arXiv preprint arXiv:2506.20183},
  year   = {2025}
}

Comments

45 pages. First part of a two-paper replacement of the original submission. Comments are welcome!

R2 v1 2026-07-01T03:32:36.798Z