TY - JOUR
T1 - Reductivity of the automorphism group of K-polystable Fano varieties
AU - Alper, Jarod
AU - Blum, Harold
AU - Halpern-Leistner, Daniel
AU - Xu, Chenyang
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00222-020-00987-2
DO - 10.1007/s00222-020-00987-2
M3 - Article
AN - SCOPUS:85088484623
SN - 0020-9910
VL - 222
SP - 995
EP - 1032
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -