Related papers: A Remark on Stability Conditions on Smooth Project…

We show that some Gieseker stable sheaves on a projective K3 surface $X$ are stable with respect to a stability condition of Bridgeland on the derived category of $X$ if the stability condition is in explicit subsets of the space of…

These are notes of a course given at the 'school on moduli spaces' at the Newton Institute in January 2011. The abstract theory of stability conditions (due to Bridgeland and Douglas) on abelian and triangulated categories is developed via…

Given a stability condition on a smooth projective variety $X$, we construct a family of stability conditions on $X\times C$, where $C$ is a smooth projective curve. In particular, this gives the existence of stability conditions on…

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…

We define a birational version of the stability of cotangent sheaves for complex projective manifolds, and more generally for smooth orbifolds. We then show, using standard conjectures in birational classification, that these cotangent…

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…

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

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's…

For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T.Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a…

This article discusses the Bridgeland stability of some sheaves on the blow-up of $\mathbb{P}^{2}$ at two general points. We have determined the destabilizing objects of the line bundles and have shown that $\mathscr{O}(E)|_{E}$ is…

We show that any extremal contraction from a smooth projective variety with dimension less than or equal to three appears as a moduli space of (semi)stable objects in the derived category of coherent sheaves.

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…

Using results in a previous paper "Non-semistable exceptional objects in hereditary categories", we focus here on studying the topology of the space of Bridgeland stability conditions on $D^b(Rep_k(Q ))$, where $Q$ is the acyclic triangular…

This note aims to clarify the deep relationship between birational modifications of a variety and semiorthogonal decompositions of its derived category of coherent sheaves. The result is a conjecture on the existence and properties of…

Let $(X,H)$ be a smooth, projective, polarized surface over $\mathbb{C}$, and let $v \in K_{\mathrm{num}}(X)$ be a class of positive rank. We prove that for certain Bridgeland stability conditions $\sigma = (\mathcal{A}, Z)$ "on the…

We study the bounded derived category $\mathcal{D}$ of an Euclidean quiver, or equivalently, that of coherent sheaves on a tame weighted projective line. We give a description of the moduli space $\mathrm{ToSS}$ of the total semi-stability…

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…

We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent…

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the…

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)…