Stable degeneration of families of klt singularities with constant local
volume
Stable degeneration of families of klt singularities with constant local
volume
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. …