On boundedness of singularities and minimal log discrepancies of Kollár components

Zhuang, Ziquan

doi:10.1090/jag/822

Author: Ziquan Zhuang
Journal: J. Algebraic Geom. 33 (2024), 521-565
DOI: https://doi.org/10.1090/jag/822
Published electronically: January 25, 2024
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Abstract | References | Additional Information

Abstract: Recent study in K-stability suggests that Kawamata log terminal (klt) singularities whose local volumes are bounded away from zero should be bounded up to special degeneration. We show that this is true in dimension three, or when the minimal log discrepancies of Kollár components are bounded from above. We conjecture that the minimal log discrepancies of Kollár components are always bounded from above, and verify it in dimension three when the local volumes are bounded away from zero. We also answer a question from Han, Liu, and Qi on the relation between log canonical thresholds and local volumes.

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Additional Information

Ziquan Zhuang
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
MR Author ID: 1257439
ORCID: 0000-0002-5466-5206
Email: zzhuang@jhu.edu

Received by editor(s): April 12, 2022
Received by editor(s) in revised form: April 7, 2023
Published electronically: January 25, 2024
Additional Notes: The author was partially supported by the NSF Grant DMS-2240926 and a Clay research fellowship.
Article copyright: © Copyright 2024 University Press, Inc.