Related papers: Product Theorem for K-stability
We prove a product formula for $\delta$-invariant and as an application, we show that product of K-(semi, poly)stable Fano varieties is also K-(semi, poly)stable.
We give a simple necessary and sufficient condition for uniform K-stability of $\mathbb{Q}$-Fano varieties.
It's well-known that adding a general boundary would create K-stability. As an application, we reprove product theorem for delta invariants of Fano varieties.
In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.
In this note, we discuss a number of open problems in K-stability theory.
We give a survey of the recent progress on the study of K-stability of Fano varieties by an algebro-geometric approach.
We study the K-stability of $\mathbb{Q}$-Fano spherical varieties using compatible divisors. More precisely, if the $\mathbb{Q}$-Fano variety, with a reductive group action, has an open Borel subgroup orbit, then there is a unique…
Tian's criterion for K-stability states that a Fano variety of dimension $n$ whose alpha invariant is greater than $\frac{n}{n+1}$ is K-stable. We show that this criterion is sharp by constructing singular Fano varieties with alpha…
We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a relation among the Seshadri constants, the alpha-invariant…
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…
We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anticanonical Q-divisors of given Fano…
In this paper, we develop an algebraic K-stability theory (e.g. special test configuration theory and optimal destabilization theory) for log Fano $\mathbb R$-pairs, and construct a proper K-moduli space to parametrize K-polystable log Fano…
We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting K\"ahler-Einstein metrics, including hypersurfaces, double solids and threefolds.
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…
We present an elementary way of recovering a well-known criterion of K-stability for Fano reductive group compactifications.
We make some observation on the logarithmic version of K-stability.
In this paper, we prove that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper.
We prove a criterion for K-stability of a $\mathbb{Q}$-Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some combinatorial data associated to the open orbit. Combined with…
We 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 existing results for usual…
We prove the following result: if a $\mathbb{Q}$-Fano variety is uniformly K-stable, then it admits a K\"{a}hler-Einstein metric. We achieve this by modifying Berman-Boucksom-Jonsson's strategy with appropriate perturbative arguments and…