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arXiv · 1906.03122

Reductivity of the automorphism group of K-polystable Fano varieties

Jarod Alper·Harold Blum·Daniel Halpern-Leistner·Chenyang Xu
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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.

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Jarod Alper, Harold Blum, Daniel Halpern-Leistner, Chenyang Xu. 2019-06-07. Reductivity of the automorphism group of K-polystable Fano varieties. https://doi.org/10.1007/s00222-020-00987-2

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