Related papers: Product theorem for K-stability

We study K-stability properties of a smooth Fano variety X using non-Archimedean geometry, specifically the Berkovich analytification of X with respect to the trivial absolute value on the ground field. More precisely, we view…

We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove that all quasi-smooth weighted Fano hypersurfaces of index 1…

In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace parametrizing reduced uniformly K-stable Fano varieties which…

In this note, we adapt the Keevash-Sudakov proof of the (Tur\'{a}n) Stability Theorem for the Fano plane to find an explicit dependency between the parameters $\varepsilon$ and $\delta$. This is useful in the solution of a multicolored…

For a given K-polystable Fano variety $X$ and a natural number $l$ such that $(X, \frac{1}{l} B)$ is log canonical for some $B\in |-lK_X|$, we show that there exists a rational number $0<c_1<1$ depending only on $X$ and $l$, such that $D\in…

We introduce a new subclass of Fano varieties (Casagrande-Druel varieties), that are $n$-dimensional varieties constructed from Fano double covers of dimension $n-1$. We conjecture that a Casagrande-Druel variety is K-polystable if the…

We introduce a new effective stability named "divisorial stability" for Fano manifolds which is weaker than K-stability and is stronger than slope stability along divisors. We show that we can test divisorial stability via the volume…

We prove that the stability condition for Fano manifolds defined by Saito-Takahashi, given in terms of the sum of the Ding invariant and the Chow weight, is equivalent to the existence of anticanonically balanced metrics. Combined with the…

We show that general one-nodal prime Fano threefolds of genus $12$ are K-polystable.

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 X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability…

We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…

Let ${\rm k}$ be an algebraically closed field of characteristic 0 and $G$ a connect, reductive group over it. Let $X$ be a projective $G$-variety of complexity 1. We classify $G$-equivariant normal test configurations of $X$ with integral…

In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log…

In this paper, we study the K-stability of polarized spherical varieties. After reduction, it can be treated as a variational problem of the reduced functional of the Futaki invariant on the associated moment polytope. With the convexity…

We study the K-moduli space of products of Fano varieties in relation to the product of K-moduli spaces of the product components. We show that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to…

Given a compact polarized manifold $(X,L)$, we introduce two new stability thresholds in terms of singularity types of global quasi-plurisubharmonic functions on $X$. We prove that in the Fano setting, the new invariants can effectively…

We prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.

We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.

We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with [Jia17,BL18], the latter result yields a separated Deligne-Mumford…