A counterexample to the PIA conjecture for minimal log discrepancies

Duke Mathematical Journal 2026 Open access

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Authors: Yusuke Nakamura, Kohsuke Shibata
DOI: 10.1215/00127094-2025-0057
Cited by: 0
References: 28

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 (lower semicontinuity) conjecture for families.

Fields of Study & Subjects

Mathematical Approximation and Integration

Publication details

Journal / source
Duke Mathematical Journal
Publisher
Duke University Press
Volume
175
Issue
10
Pages
1715–1736
Publication date
15 July 2026
Language
EN