Related papers: Introduction to stability conditions
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…
In these lecture notes we give an introduction to Bridgeland stability conditions on smooth complex projective varieties with a particular focus on the case of surfaces. This includes basic definitions of stability conditions on derived…
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…
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 propose the notion of stability on a triangulated category that is a generalization of the T.Bridgeland's stability data. We establish connections between stabilities and t-structures on a category and as application we get the…
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…
Categorical resolutions of singularities are a replacement of resolution of singularities within the realm of triangulated categories. They allow the study of the derived category of a singular variety $X$ via a triangulated category that…
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…
The space of stability conditions on a triangulated category is naturally partitioned into subsets $U(A)$ of stability conditions with a given heart $A$. If $A$ has finite length and $n$ simple objects then $U(A)$ has a simple geometry,…
We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This approach is based on the notion of a perverse…
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 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)…
Let $C$ be a smooth projective curve of genus $g>0$. We describe an open locus of Bridgeland stability conditions on the bounded derived category of coherent systems on $C$, and show that stability manifold detects the Brill--Noether theory…
We study stability conditions induced by functors between triangulated categories. Given a finite group acting on a smooth projective variety we prove that the subset of invariant stability conditions embeds as a closed submanifold into the…
We introduce the notion of relative stability conditions on triangulated categories with respect to left admissible subcategories, based on arXiv:math/0212237, and demonstrate the deformation of relative stability conditions via the…
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and…
T. Bridgeland defined the notion of a stability manifold for a triangulated category, motivated by Douglas's work on \Pi-stability for D-branes. We show that the stability manifold of the bounded derived category of the coherent sheaves on…
In this work more questions arise than answers given, for which of course we do not apologize. The core of this paper is concerned with the construction of a ``constant'' t-structure on the bounded derived category of coherent sheaves…
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…
This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand…