Stable degeneration of families of klt singularities with constant local volume
arXiv:2405.19273 · doi:10.1017/fms.2025.10111
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.
38 pages, an example is added