Related papers: A note on the definition of K-stability

Mabuchi solitons generalize K\"{a}hler-Einstein metrics on Fano manifolds, which constitute a Yau-Tian-Donaldson type correspondence with relative Ding stability. Comparing with K\"{a}hler-Ricci solitons, there is a distinct necessary…

We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the K\"ahler cone of any compact K\"ahler manifold, thus establishing an algebro-geometric…

We prove structure theorems for the Donaldson invariants of 4-manifolds with b_+=1, similar to those of Kronheimer and Mrowka in the case b_+>1: We show that for a 4-manifold with b_+=1 and two different period points F, G on the boundary…

We consider $k$-positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to positive linear systems. It is well-known that stable positive linear time…

Let $X$ be a compact K\"ahler manifold and $\alpha$ a K\"ahler class on $X$. We prove that if $(X,\alpha)$ is uniformly K-stable for models, then there is a unique cscK metric in $\alpha$. This was first proved in the algebraic case by Chi…

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…

For a given polarized toric variety, we define the notion of $\lambda$-stability which is a natural generalization of uniform K-stability. At the neighbourhoods of the vertices of the corresponding moment polytope $\Delta$, we consider…

We study the existence and stability of Q-balls in noncanonical scalar field theories, $K(|\Phi|^2,X)$ where $\Phi$ is the complex scalar field and $X$ is the kinetic term. We extend the Vakhitov-Kolokolov stability criterion to K-field…

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a…

In this note, we prove that on polarized toric manifolds the relative $K$-stability with respect to Donaldson's toric degenerations is a necessary condition for the existence of Calabi's extremal metrics, and also we show that the modified…

Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of quantities associated to valuations, which has been essential to all recent progress in the area. We introduce a notion of valuative stability for…

In this paper, we establish characterizations of variational $s$-convexity and tilt stability for prox-regular functions in the absence of subdifferential continuity via quadratic bundles, a kind of primal-dual generalized second-order…

We prove that, for a spherical Fano threefold not in the Mori-Mukai family 2-29, and a weight function associated with the action of the connected center of a Levi subgroup of its automorphism group, weighted K-polystability is equivalent…

We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying…

If $M$ is a projective manifold in $P^N$, then one can associate to each one parameter subgroup $H$ of $SL(N+1)$ the Mumford $\mu$ invariant. The manifold $M$ is Chow-Mumford stable if $\mu$ is positive for all $H$. Tian has defined the…

The Hitchin-Kobayashi correspondence for vector bundles, established by Donaldson, Kobayashi, Luebke, Uhlenbeck and Yau, states that an indecomposable holomorphic vector bundle over a compact Kaehler manifold is stable in the sense of…

In this note we identify the leading terms of the (reduced) K-energy map with a universal linear combination of the principal and subdominant coefficients of the weight of the $mth$ Hilbert point. This shows that the weight…

We define a Fourier-Mukai transform for sheaves on K3 surfaces over $\C$, and show that it maps polystable bundles to polystable ones. The role of ``dual'' variety to the given K3 surface $X$ is here played by a suitable component $\hat X$…

This paper investigates stable cohomotopy groups in codimensions two and three from complementary algebraic and geometric viewpoints. For general CW complexes, we give a complete characterization of stable cohomotopy in codimension two and…

The main result of this paper is the statement that the Hodge theoretic Donaldson-Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure…