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arXiv · 2003.13788

K-stability of Fano varieties via admissible flags

Hamid Abban·Ziquan Zhuang
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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 K\"ahler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) to compute the stability thresholds for hypersurfaces at generalized Eckardt points and for cubic surfaces at all points, and (c) to provide a new algebraic proof of Tian's criterion for K-stability, amongst other applications.

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Hamid Abban, Ziquan Zhuang. 2020-03-30. K-stability of Fano varieties via admissible flags. https://arxiv.org/abs/2003.13788

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