K-stability of Fano varieties via admissible flags

By Hamid Abban, Ziquan Zhuang. Forum of Mathematics, Pi, 2020

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Abstract 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.

Subfields: Applied Mathematics, Geometry and Topology

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