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arXiv · 2405.19273

Stable degeneration of families of klt singularities with constant local volume

Zhiyuan Chen
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Abstract

We prove that for a locally stable family of klt singularities with constant local volume, the ideal sequences of the minimizing valuations for the normalized volume function form a family of ideals with flat cosupport, which induces a degeneration to a locally stable family of K-semistable log Fano cone singularities. Our proof is a family version of the method of C. Xu and Z. Zhuang proving finite generation by Koll\'ar models and multiple degenerations.

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Zhiyuan Chen. 2024-05-29. Stable degeneration of families of klt singularities with constant local volume. https://doi.org/10.1017/fms.2025.10111

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