Reductivity of the automorphism group of K-polystable Fano varieties

Jarod Alper; Harold Blum; Daniel Halpern-Leistner; Chenyang Xu

doi:10.1007/s00222-020-00987-2

Reductivity of the automorphism group of K-polystable Fano varieties

Jarod Alper
, Harold Blum
, Daniel Halpern-Leistner
, Chenyang Xu

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

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.

Original language	English (US)
Pages (from-to)	995-1032
Number of pages	38
Journal	Inventiones Mathematicae
Volume	222
Issue number	3
DOIs	https://doi.org/10.1007/s00222-020-00987-2
State	Published - Dec 1 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-020-00987-2

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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 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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AU - Blum, Harold

AU - Halpern-Leistner, Daniel

AU - Xu, Chenyang

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Y1 - 2020/12/1

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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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Reductivity of the automorphism group of K-polystable Fano varieties

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