Reductivity of the automorphism group of K-polystable Fano varieties

• 成果类型: Article
• 署名作者: Alper, Jarod; Blum, Harold; Halpern-Leistner, Daniel; Xu, Chenyang
• 署名单位: University of Washington; University of Washington Seattle; Utah System of Higher Education; University of Utah; Cornell University; Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00987-2
• 发表日期: 2020
• 页码: 995-1032
• 关键词: kahler-einstein metrics; MODULI SPACES; STABILITY; EXISTENCE; volume

摘要

We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Theta-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space.