Related papers: K-moduli with real coefficients

We study K-stability of products of K-stable $\mathbb{Q}$-Fano varieties.

In this article, we completely determine which log Fano hyperplane arrangements are uniformly K-stable, K-stable, K-polystable, K-semistable or not.

We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show…

Let $G$ be a connected, complex reductive group. In this paper, we classify $G\times G$-equivariant normal $\mathbb R$-test configurations of a polarized $G$-compactification. Then for $\mathbb Q$-Fano $G$-compactifications, we express the…

We prove various results involving arcs - which generalise test configurations - within the theory of K-stability. Our main result characterises coercivity of the Mabuchi functional on spaces of Fubini-Study metrics in terms of uniform…

We prove several boundedness results for log Fano pairs with certain K-stability. In particular, we prove that K-semistable log Fano pairs of Maeda type form a log bounded family. We also compute K-semistable domains for some examples.

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…

We prove that every birationally superrigid Fano variety whose alpha invariant is greater than (resp. no smaller than) $\frac{1}{2}$ is K-stable (resp. K-semistable). We also prove that the alpha invariant of a birationally superrigid Fano…

For any log Fano pair with a torus action, we associate a computable invariant to it, such that the pair is (weighted) K-polystable if and only if this invariant is greater than one. As an application, we present examples of Fano varieties…

We study the stabilization behavior of cohomology groups associated with moduli spaces of quiver representations for a fixed quiver $Q$. Under mild conditions on a dimension vector $\delta$, we show that the dimensions of these cohomology…

For any flat projective family $(\mX,\mL)\rightarrow C$ such that the generic fibre $\mX_\eta$ is a klt Q-Fano variety and $\mL|_{\mX_\eta}\sim_{Q}-K_{X_{\eta}}$, we use the techniques from the minimal model program (MMP) to modify the…

We introduce a notion of K-stability for adjoint foliated structures via test configurations and the foliated Donaldson-Futaki invariant. We prove reduction to special test configurations for adjoint Fano foliated structures by showing that…

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 find Fano threefolds $X$ admitting K\"ahler-Ricci solitons (KRS) with non-trivial moduli, which are $\mathbb{T}$-varieties of complexity two. More precisely, we show that the weighted K-stability of $(X,\xi_0)$ (where $\xi_0$ is the…

We compute the $\delta$-invariant for pairs $(\mathbb{P}^2, \lambda C_d)$, where $C_d$ is a plane curve of degree $d \leq 4$. These computations provide new examples of $K$-stable and $K$-semistable log Fano pairs, and contribute to the…

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…

We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.

We prove two new results on the K-polystability of Q-Fano varieties based on purely algebro-geometric arguments. The first one says that any K-semistable log Fano cone has a special degeneration to a uniquely determined K-polystable log…

We explicitly determine the optimal degenerations of Fano threefolds $X$ in family No 2.23 of Mori-Mukai's list as predicted by the Hamilton-Tian conjecture. More precisely, we find a special degeneration $(\mathcal{X}, \xi_0)$ of $X$ such…

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…