Stable degenerations of singularities

2022/05/22 by Chenyang Xu, Xu, Chenyang, Ziquan Zhuang +1 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2205.10915

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.

Cited by

• Optimal bounds for local volumes of threefold singularities
• Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra

Related

• Stable degeneration of families of klt singularities with constant local volume
• Stability of klt singularities
• Stability of Valuations: Higher Rational Rank
• Uniqueness of the minimizer of the normalized volume function
• Finite generation for valuations computing stability thresholds and applications to K-stability