Reductivity of the automorphism group of K-polystable Fano varieties
Reductivity of the automorphism group of K-polystable Fano varieties
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DOI：
10.1007/s00222-020-00987-2
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发表时间：
2019-06
影响因子：
3.1
通讯作者：
J. Alper;Harold Blum;Daniel Halpern-Leistner;Chenyang Xu-
中科院分区：
文献类型：
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作者：
J. Alper;Harold Blum;Daniel Halpern-Leistner;Chenyang Xu-
证明了K-多稳定对数Fano对有约化自同构群。事实上，我们通过建立关于K-半稳定对数Fano对的模的S完备性和-可约性的更一般的结果来推导这一命题。在K-半稳定猜想是开条件的前提下，证明了K-半稳定Fano簇的Artin堆栈参数化模空间是可分的。
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-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.