Related papers: Stability conditions under change of base field

We provide examples of an explicit submanifold in Bridgeland stabilities space of a local Calabi-Yau, and propose a new variant of definition of stabilities on a triangulated category, which we call a "real variation of stability…

We construct a topological embedding of the maximal connected component of Bridgeland stability conditions of a (twisted) Abelian surface into the distinguished connected component of the stability manifold of the associated (twisted)…

Bridgeland stability condition is preserved under the Fourier-Mukai transform by its definition. We explain the relation with Gieseker stability. By studying the wall-crossing behavior, we reprove that the moduli spaces of stable sheaves on…

Let $X$ be a smooth complex projective variety. In 2002, Bridgeland defined a notion of stability for the objects in $D^b(X)$, the bounded derived category of coherent sheaves on $X$, which generalized the notion of slope stability for…

We construct Bridgeland stability conditions on the the following hyper-K\"ahler or strict Calabi--Yau manifolds: - Generalized Kummer varieties associated to an abelian surface that is isogenous to a product of elliptic curves. - Universal…

We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.

We prove the conjectural Bogomolov-Gieseker type inequality for tilt slope stable objects on each Fano threefold X of Picard number one. Based on the previous works on Bridgeland stability conditions, this induces an open subset of…

The key result in the theory of Bridgeland stability conditions is the property that they form a complex manifold. This comes from the fact that given any small deformation of the central charge, there is a unique way to correspondingly…

We give a natural family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe ``wall-crossing behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates Pic(S)…

In this paper, we prove BG-type inequality conjecture for threefolds in the title. In particular, there exist Bridgeland stability conditions on these threefolds.

Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a "real variation of stability conditions" (which is related to Bridgeland's stability conditions), and construct an example using categories of coherent sheaves on…

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 give a complete description of the Bridgeland stability manifold for the bounded derived category of holomorphic triples over a smooth projective curve of genus 1 as a connected, four dimensional complex manifold.

Let $K$ be a local field and let $L/K$ be a totally ramified Galois extension of degree $p^n$. Being semistable and possessing a Galois scaffold are two conditions which facilitate the computation of the additive Galois module structure of…

For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are…

The space of Bridgeland stability conditions is a complex manifold that can be attached to a triangulated category, of which it encodes some homological properties. These notes are an introduction to this topic, with a focus on examples…

We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we…

We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The…

Let $X$ be a smooth compact complex surface with the canonical divisor $K_X$ ample and let $\Theta_X$ be its holomorphic tangent bundle. Bridgeland stability conditions are used to study the space $H^1 (\Theta_X)$ of infinitesimal…

We define and study a gluing procedure for Bridgeland stability conditions in the situation when a triangulated category has a semiorthogonal decomposition. As an application we construct stability conditions on the derived categories of…