相关论文: Stability conditions on curves
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…
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 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…
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…
We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with…
In this paper we describe a simply connected component of the complex manifold of stability conditions on the bounded derived category of a generic complex torus of any dimension. A torus is called generic if there are no nontrivial…
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…
Inspired by Schmidt's work on twisted cubics, we study wall crossings in Bridgeland stability, starting with the Hilbert scheme $\mathrm{Hilb}^{2m+2}(\mathbb{P}^3)$ parametrizing pairs of skew lines and plane conics union a point. We find…
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…
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…
Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…
We apply results on inducing stability conditions to local Calabi-Yau threefolds and obtain applications to Donaldson-Thomas (DT) theory. A basic example is the total space of the canonical bundle of $Z=\mathbb{P}^1\times \mathbb{P}^1$. We…
We investigate the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters constructed by Bridgeland. For a stable sheaf, we give effective bounds of these…
We show that, under mild conditions, the space of numerical Bridgeland stability conditions Stab(T) on a triangulated category T is complete. In particular the metric on a full component of Stab(T) for which the central charges factor…
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…
We show that the locally free sheaf of locally exact differentials on a smooth projective curve of genus at least two over an algebraically closed field k of characteristic p is a stable vector bundle. This answers a question of Raynaud.
In this survey we borrow from Coskun and Huizenga an example of application of Bridgeland stability conditions to birational geometry and we rephrase it without assuming any previous knowledge about derived categories.
We introduce a new class of triangulated categories, which are Verdier quotients of three-Calabi-Yau categories from (decorated) marked surfaces, and show that its spaces of stability conditions can be identified with moduli spaces of…
Inspired by mirror symmetry, we investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to develop theory of Weil-Petersson geometry on the stringy…
An object in the bounded derived category D^b(Coh(X)) of coherent sheaves on a complex projective K3 surface X is spherical if it is rigid and simple. Although spherical objects form only a discrete set in the moduli stack of complexes,…