A counterexample to the PIA conjecture for minimal log discrepancies
Algebraic Geometry
2026-05-01 v4
Abstract
We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.
Cite
@article{arxiv.2404.06164,
title = {A counterexample to the PIA conjecture for minimal log discrepancies},
author = {Yusuke Nakamura and Kohsuke Shibata},
journal= {arXiv preprint arXiv:2404.06164},
year = {2026}
}
Comments
14 pages. In v3, the paper is streamlined by introducing a new concept called "virtually free action". To appear in Duke Math. J