Stable degenerations of singularities
Algebraic Geometry
2025-01-20 v2 Commutative Algebra
Differential Geometry
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.
Cite
@article{arxiv.2205.10915,
title = {Stable degenerations of singularities},
author = {Chenyang Xu and Ziquan Zhuang},
journal= {arXiv preprint arXiv:2205.10915},
year = {2025}
}
Comments
42 pages. Accepted version. To appear in JAMS