K-stabilityFano varietiesWe develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Khler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised...
Fano varietyEquivariant K-stabilityPseudovaluationValuative criterionNormalized volumeWe define G -pseudovaluations on a variety with a group action G . By introducing G -pseudovaluations, we are able to give some criteria for G -equivariant K-stability of Fano varieties which are parallel to ...
using the recently constructed moduli spaces of log fano pairs from the theory of k-stability. we note that the analogous question in the case of epw sextics remains open, and it would be interesting to try to use k-moduli to study their compactifications. for a rational number \(c\in ...
Here we consider its relation with K-semistability, which is animportant concept in the study of K\"{a}hler-Einstein metrics on Fanovarieties. In particular, we prove that for a $\\mathbb{Q}$-Fano variety $V$,the K-semistability of $(V, -K_V)$ is equivalent to the condition that...
We introduce a new subclass of Fano varieties (Casagrande–Druel varieties) that are -dimensional varieties constructed from Fano double covers of dimension n1 . We conjecture that a Casagrande–Druel variety is K-polystable if the double cover and its base space are K-polystable. We prove ...
We prove that it is at least a sufficient condition and also related to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.Fujita, KentoOdaka, Yuji...
Alpha invariants and K-stability for general polarizations of Fano varieties, Int. Math. Res. Not. IMRN (2015), no. 16, 7162-7189. MR 3428958R. Dervan, Alpha invariants and K-stability for general polarizations of Fano varieties, Int. Math. Res. Not. IMRN 16 (2015), 7162-7189....
Proceedings of the London Mathematical SocietyFjt16a] K. Fujita, On K-stability and the volume functions of Q-Fano varieties, Proc. Lond. Math. Soc. 113 (2016), no. 5, 541-582.Fuj15a] K. Fujita, On K-stability and the volume functions of Q-Fano varieties, Proc. Lon- don Math. ...
Xu. "Special test configuration and K-stability of Fano varieties". Ann. of Math. (2) 180 (2014), no. 1, 197-232.C. Li, and C. Xu, Special test configurations and K-stability of Fano varieties, Ann. of Math. (2) 180 (2014), no.1, 197-232....
As a consequence, we obtain several explicit examples of K-stable Fano varieties admitting (singular) Khler-Einstein metrics. We also compute the greatest Ricci lower bounds, equivalently the delta invariants for K-unstable varieties. This gives us three new examples on which each solution of the...