On boundedness of singularities and minimal log discrepancies of Kollár components, II

Zhuang, Ziquan

doi:10.2140/gt.2024.28.3909

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On boundedness of singularities and minimal log discrepancies of Kollár components, II

Ziquan Zhuang

Geometry & Topology 28 (2024) 3909–3933

DOI: 10.2140/gt.2024.28.3909

Abstract

We show that a set of K–semistable log Fano cone singularities is bounded if and only if their local volumes are bounded away from zero, and their minimal log discrepancies of Kollár components are bounded from above. As corollaries, we confirm the boundedness conjecture for K–semistable log Fano cone singularities in dimension three, and show that local volumes of $3$ –dimensional klt singularities only accumulate at zero.

Keywords

boundedness, klt singularities, moduli, K-stability, normalized volume, Kollár component

Mathematical Subject Classification

Primary: 14B05, 14E99, 14J45

References

Publication

Received: 20 February 2023

Revised: 2 October 2023

Accepted: 23 December 2023

Published: 20 December 2024

Proposed: Dan Abramovich

Seconded: Mark Gross, Gang Tian

Authors

Ziquan Zhuang
Department of Mathematics Johns Hopkins University Baltimore, MD United States

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Volume 28, issue 8 (2024)