Related papers: Gepner type stability conditions on graded matrix …

Conditions for the existence and stability of de Sitter space in modified gravity are derived by considering inhomogeneous perturbations in a gauge-invariant formalism. The stability condition coincides with the corresponding condition for…

In this paper, we study the action of an autoequivalence, the spherical twist associated to a torsion sheaf, on the standard Bridgeland stability conditions and a generalized weak stability condition on the derived category of a K3 surface.…

Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories…

The derived category of coherent systems is an interesting triangulated category associated with a smooth, projective curve $C$. These categories admit Bridgeland stability conditions, as recently shown by Feyzbakhsh and Novik. Their…

Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in…

Let $(X,H)$ be a smooth, projective, polarized surface over $\mathbb{C}$, and let $v \in K_{\mathrm{num}}(X)$ be a class of positive rank. We prove that for certain Bridgeland stability conditions $\sigma = (\mathcal{A}, Z)$ "on the…

In [Ma1] S. Ma established a bijection between Fourier--Mukai partners of a K3 surface and cusps of the K\"ahler moduli space. The K\"ahler moduli space can be described as a quotient of Bridgeland's stability manifold. We study the…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 3. We show that their moduli space is birational to the blow-up at a special point of a certain…

We show how matrix problems (bimodule categories) can be used in studying triangulated categories. Then we apply the general technique to the classification of stable homotopy types of polyhedra, find out the "representation types" of such…

We provide an algorithm for calculating the unramified Brauer group of a homogeneous space $X$ of a semi-simple simply connected group $H$ with finite geometric stabiliser over any field of characteristic 0. When $k$ is a number field, we…

We give some remarks on our papers with Minamide and Yanagida on Bridgeland stability conditions. We also give a remark on stability conditions on Enriques surfaces, and give another proof of the projectivity of the coarse moduli spaces of…

We introduce stability conditions (in the sense of King) for representable modules of continuous quivers of type A along with a special criteria called the four point condition. The stability conditions are defined using a generalization of…

We study multiple orthogonal polynomials of type I and type II which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the…

We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…

We define a category of filtered topological spaces and explore some of its homotopy theoretic properties, including a filtered analogue of CW approximation. With this, we define and study a filtered (weighted) variant of the Euler…

We show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are proper algebraic stacks of finite type, if they satisfy the Bogomolov-Gieseker (BG for short) inequality conjecture proposed by Bayer, Macr\`i…

Let $X$ be a smooth projective variety over $\mathbb C$. In this paper, we prove that $\mathrm{D}^b(X)$, the bounded derived category of coherent sheaves on $X$, always admits stability conditions in the sense of Bridgeland.

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 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…

We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The…