Related papers: Stability conditions on curves
We study the space of stability conditions on the total space of the canonical line bundle over the three dimensional projective space. We construct a family of geometric stability conditions and some subset of the boudary of them, which…
We describe the spaces of stability conditions on certain triangulated categories associated to Dynkin diagrams. These categories can be defined either algebraically via module categories of preprojective algebras, or geometrically via…
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…
We describe spaces of Bridgeland stability conditions on certain triangulated categories associated to Coxeter systems. These categories are defined algebraically using the category of modules for zigzag algebras associated to Coxeter…
We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which…
We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri and Toda for some products of three curves. This gives the first examples of Bridgeland stability conditions on some threefolds of general type. The key ingredients…
On objects of a triangulated category with a stability condition, we construct a topology.
We introduce the notion of a polynomial stability condition, generalizing Bridgeland stability conditions on triangulated categories. We construct and study a family of polynomial stability conditions for any normal projective variety. This…
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 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…
This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover…
We study concepts of stabilities associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the associated Dual Span Bundle and linear stability. Our result…
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…
In this paper, we give a definition of weak stability condition on a triangulated category. The difference between our definition and existing definitions is that we allow objects in the kernel to have non-maximal phases. We then construct…
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)…
We discuss potential (largely speculative) applications of Bridgeland's theory of stability conditions to symplectic mapping class groups.
We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves. As an application, we construct stability conditions on…
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the…
We prove a new version of Bogomolov's inequality on normal proper surfaces. This allows to construct Bridgeland's stability condition on such surfaces. In particular, this gives the first known examples of stability conditions on…
A triangulated category $\mathcal{C}$ with a canonical Bott's isomorphism $[2]\xrightarrow{\sim}id$ is called a cyclic category in this paper. We give a new notion of stability conditions on a $k$-linear Krull-Schmidt cyclic category. Given…