Uniqueness of K-polystable degenerations of Fano varieties

• 成果类型: Article
• 署名作者: Blum, Harold; Xu, Chenyang
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.190.2.4
• 发表日期: 2019
• 页码: 609-656
• 关键词: kahler-einstein metrics; MODULI SPACES; scalar curvature; STABILITY; EXISTENCE; volume; VALUATIONS

摘要

We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with recently proven boundedness and openness statements, the latter result yields a separated Deligne-Mumford stack parametrizing all uniformly K-stable Q-Fano varieties of fixed dimension and volume. The result also implies that the automorphism group of a K-stable Q-Fano variety is finite.