Reductivity of the automorphism group of K-polystable Fano varieties

Jarod Alper, Harold Blum, Daniel Halpern-Leistner, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 Θ -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.

Original languageEnglish (US)
Pages (from-to)995-1032
Number of pages38
JournalInventiones Mathematicae
Issue number3
StatePublished - Dec 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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