Related papers: Quadratic differentials as stability conditions: c…
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…
We study the categorification of collapsed Riemann surfaces with quadratic differentials allowing arbitrary order zeros and poles via the Verdier quotient. We establish an isomorphism between the exchange graph of hearts in the quotient…
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…
Categorically, we introduce the Calabi-Yau-$\mathbb{X}$ categories $\mathcal{D}_{\mathbb{X}}$ of a graded marked surface $\mathbf{S}^\lambda$, as a $q$-deformation of the topological Fukaya category $\mathcal{D}_\infty$ of…
We study a class of triangulated categories obtained as Verdier quotients of 3-Calabi-Yau categories combinatorially described by quivers with potential from (decorated) marked surfaces. We study their bounded t-structures and consider in…
We consider a 3-Calabi-Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps between Riemann surfaces, we construct a natural map from a component of the space of…
In this paper, we study the space of stability conditions on a certain $N$-Calabi-Yau ($\text{CY}_N$) category associated to an $A_n$-quiver. Recently, Bridgeland and Smith constructed stability conditions on some $\text{CY}_3$ categories…
We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is…
We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasi-projective 3-folds associated to meromorphic quadratic differentials. Together…
A (meromorphic) quadratic differential is a (meromorphic) section of the tensor square of the canonical bundle of a Riemann surface. They arose in the study of quasiconformal mappings in the works of Oswald Teichm\"uller, and have played a…
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…
In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian) fibrations. In…
We prove that the principal component of the exchange graph of hearts of a graded skew-gentle algebra can be identified with the corresponding exchange graph of S-graphs, using the geometric models and the intersection formula in…
We construct stability conditions on crepant resolutions of certain quotients of product varieties, giving as a special case the first examples of stability conditions on strict Calabi-Yau varieties of arbitrary dimension. Along the way, we…
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 introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calabi--Yau structure. We discovered these algebras through two…
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…
In this paper, we describe the spaces of stability conditions on the triangulated categories associated to three dimensional crepant small resolutions. The resulting spaces have chamber structures such that each chamber corresponds to a…
These are notes of a course given at the 'school on moduli spaces' at the Newton Institute in January 2011. The abstract theory of stability conditions (due to Bridgeland and Douglas) on abelian and triangulated categories is developed via…
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…