Optimal destabilizing centers and equivariant K-stability

We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano...

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Bibliographic Details
Published inInventiones mathematicae Vol. 226; no. 1; pp. 195 - 223
Main Author Zhuang, Ziquan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Springer Nature B.V
Subjects
Algebra
Mathematics
Mathematics and Statistics
Theorems
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Summary:We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano pairs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-021-01046-0