Related papers: Stability conditions on cyclic categories I: basic…
For the Fermat Calabi-Yau threefold and the theory of stability conditions [Bri07], there have been two mathematical aims given by physical reasoning. One is that we should define stability conditions by central charges of quintic periods…
Let $\mathcal{C}$ be a triangulated category. We first introduce the notion of balanced pairs in $\mathcal{C}$, and then establish the bijective correspondence between balanced pairs and proper classes $\xi$ with enough $\xi$-projectives…
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…
We introduce the notion of Gepner type Bridgeland stability conditions on triangulated categories, which depends on a choice of an autoequivalence and a complex number. We conjecture the existence of Gepner type stability conditions on the…
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…
We prove that any `finite-type' component of a stability space of a triangulated category is contractible. The motivating example of such a component is the stability space of the Calabi--Yau-$N$ category $\mathcal{D}(\Gamma_N Q)$…
We present a notion of $\Delta$-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the existence of a zero morphism, a…
Let $X$ be a surface with an ADE-singularity and let $\widetilde{X}$ be its crepant resolution. In this paper, we show that there exists a Bridgeland stability condition $\sigma_X$ on ${\rm D}^b(X)$ and a weak stability condition…
We construct a geometric model for the root category $\mathcal{D}^b(Q)/[2]$ of any Dynkin diagram $Q$, which is an $h_Q$-gon $\mathbf{V}_Q$ with cores, where $h_Q$ is the Coxeter number and $\mathcal{D}^b(Q)$ is the bounded derived category…
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…
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 show the existence of Gepner type Bridgeland stability conditions on the triangulated categories of graded matrix factorizations associated with homogeneous polynomials which define general cubic fourfolds containing a plane. The key…
A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual. The unit and counit satisfy the usual "zig-zag" identities of a compact closed category only up to natural isomorphism, and the…
We show that the conjectural construction proposed by Bayer, Bertram, Macr\'i and Toda gives rise to Bridgeland stability conditions for a principally polarized abelian three-fold with Picard rank one by proving that tilt stable objects…
If $G$ is a group acting geometrically on a CAT(0) cube complex $X$ and if $g \in G$ is an infinite-order element, we show that exactly one of the following situations occurs: (i) $g$ defines a rank-one isometry of $X$; (ii) the stable…
We study the Bridgeland stability of line bundles on surfaces using Bridgeland stability conditions determined by divisors. We show that given a smooth projective surface $S$, a line bundle $L$ is always Bridgeland stable for those…
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…
It follows from a theorem of Gromov that the stable systolic category of a closed manifold is bounded from below by the rational cup-length of the manifold. In the paper we study the inequality in the opposite direction. In particular,…
We give a brief introduction to the relationship between Bridgeland stability conditions and the $K(\pi,1)$ conjecture for Artin groups. These notes have been written as pre-reading for the MFO mini-workshop 2405a: Artin groups meet…
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…