Reductivity of the automorphism group of K-polystable Fano varieties
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Author(s)
Alper, Jarod
Blum, Harold
Halpern-Leistner, Daniel
Xu, Chenyang
Date Issued
July 2020
Journal
Inventiones mathematicae
Publisher
Springer Berlin Heidelberg
Citation
Alper, Jarod et al. "Reductivity of the automorphism group of K-polystable Fano varieties." Inventiones mathematicae 220 (July 2020): 995–1032 © 2020 Springer-Verlag
Version
Author's final manuscript
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 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00222-020-00987-2
