Stable degeneration of families of klt singularities with constant local volume

2024/05/29 by Chen, Zhiyuan · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.19273

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 Kollár models and multiple degenerations.

Cited by

• On Sun-Zhang's theory of Fano fibrations -- weighted volumes, moduli and bubbling Fano fibrations

Related

• Stable degenerations of singularities
• Stability of Valuations: Higher Rational Rank
• Stability of klt singularities
• Finite generation for valuations computing stability thresholds and applications to K-stability
• Boundedness of log Fano cone singularities and discreteness of local volumes