Reductivity of the automorphism group of K-polystable Fano varieties
Abstract
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.
- Publication:
-
Inventiones Mathematicae
- Pub Date:
- December 2020
- DOI:
- 10.1007/s00222-020-00987-2
- arXiv:
- arXiv:1906.03122
- Bibcode:
- 2020InMat.222..995A
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Differential Geometry
- E-Print:
- 32 pages. Final version. To appear in Inventiones Math