K-stability of Fano varieties via admissible flags

We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic su...

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Bibliographic Details
Published inForum of mathematics. Pi Vol. 10
Main Authors Abban, Hamid, Zhuang, Ziquan
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.2022
Subjects
14J45
32Q20
Algebraic and Complex Geometry
Fano varieties
Hyperspaces
K-stability
Stability criteria
14J45
K-stability
32Q20
Fano varieties
Online AccessGet full text
ISSN2050-5086
2050-5086
DOI10.1017/fmp.2022.11

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Summary:We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic surfaces at all points, and (c) provide a new algebraic proof of Tian’s criterion for K-stability, amongst other applications.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:2050-5086
2050-5086
DOI:10.1017/fmp.2022.11