Stable degenerations of singularities

Xu, Chenyang; Zhuang, Ziquan

doi:10.1090/jams/1055

Stable degenerations of singularities
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by Chenyang Xu and Ziquan Zhuang;

J. Amer. Math. Soc. 38 (2025), 585-626

DOI: https://doi.org/10.1090/jams/1055

Published electronically: January 29, 2025

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Abstract:

For any Kawamata log terminal (klt) singularity and any minimizer of its normalized volume function, we prove that the associated graded ring is always finitely generated, as conjectured by Chi Li. As a consequence, we complete the last step of establishing the Stable Degeneration Conjecture proposed by Chi Li and the first named author for an arbitrary klt singularity.

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Stable degenerations of singularities
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Abstract: