Related papers: Stability conditions for contraction algebras
Let $f\colon X\to\mathrm{Spec}\, R$ be a 3-fold flopping contraction, where $X$ has at worst Gorenstein terminal singularities and $R$ is complete local. We describe the space of Bridgeland stability conditions on the null subcategory…
We find stability conditions ([Do], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent…
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…
Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied…
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 show that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. has a length heart with finitely many simple objects. As a corollary, we obtain that the space of Bridgeland stability…
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.
Consider a 2-Calabi--Yau triangulated category with a Bridgeland stability condition. We devise an effective procedure to reduce the phase spread of an object by applying spherical twists. Using this, we give new proofs of the following…
We study the space of stability conditions attached to the derived category of $A_{n}$-mod for $A_{n}$ the Brauer tree algebra of the line with $n$ edges. These algebras arise in the study of cyclic defect blocks of group algebras, and they…
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…
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)…
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…
Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, homological stability…
The goal of this paper is to study the subspace of stability condition $\Sigma_{\mathcal{E}}\subset \mathrm{Stab}(X)$ associated to an exceptional collection $\mathcal{E}$ on a projective variety $X$. Following Emanuele Macr\`{i}'s…
The space of Bridgeland stability conditions on the bounded derived category of coherent sheaves on P2 has a principle connected component Stab^\dag(P2). We show that Stab^\dag(P2) is the union of geometric and algebraic stability…
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…
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…
Given a triangulated category $\mathcal{C}$, we construct a partial compactification, denoted $\mathcal{A}\mathrm{Stab}(\mathcal{C})$, of the quotient of its stability manifold by $\mathbb{C}$. The purpose of…
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 describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following…