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تسجيل مستخدم جديدK-stability of Fano varieties: an algebro-geometric approach
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تأليف
Chenyang Xu
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We give a survey of the recent progress on the study of K-stability of Fano varieties by an algebro-geometric approach.
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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 Kahler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) to compute the stability thresholds for hypersu
rfaces at generalized Eckardt points and for cubic surfaces at all points, and (c) to provide a new algebraic proof of Tians criterion for K-stability, amongst other applications.
We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano 3-fold with obstructed deformations. In one case, the K-moduli space
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