Geodesic
K-stability of Fano varieties via admissible flags
Forum of Mathematics, Pi, Tome 10 (2022)

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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. 
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     author = {Hamid Abban and Ziquan Zhuang},
     title = {K-stability of {Fano} varieties via admissible flags},
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Hamid Abban; Ziquan Zhuang. K-stability of Fano varieties via admissible flags. Forum of Mathematics, Pi, Tome 10 (2022). doi: 10.1017/fmp.2022.11

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