Stable degenerations of singularities

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.

K-stability for varieties with a big anticanonical class

“…Theorem 1.2 says K-stability is indeed the same as uniform K-stability. For a log Fano pair, this is proved in [LXZ22] (see [XZ22] for a different proof).…”

K-stability for varieties with a big anticanonical class

“…Theorem 1.2 is saying K-stability is indeed the same as uniform K-stability. For a log Fano pair, this is proved in [LXZ22] (see [XZ22] for a different proof).…”