Related papers: T-stabilities for a weighted projective line
We study stability conditions on the derived categories of coherent sheaves on some projective varieties. We give a complete description of the stability manifold for smooth projective curves and we examine a connected open subset of the…
The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular…
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…
In this paper we introduce a local-refinement procedure to investigate stability data on an abelian category, and provide a sufficient and necessary condition for a stability data to be finest. We classify all the finest stability data for…
In this paper, we prove BG-type inequality conjecture for threefolds in the title. In particular, there exist Bridgeland stability conditions on these threefolds.
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…
We generalize the framework of tilt-stability to singular schemes and formulate the generalized Bogomolov-Gieseker inequality conjecture of Bayer-Macr\`i-Toda for singular threefolds. We also develop relative versions of these…
We propose compactifications of the moduli space of Bridgeland stability conditions of a triangulated category. Our construction arises from a viewing a stability condition as a metric on the underlying category and is inspired by the…
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The…
For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are…
The paper contains general results on the uniqueness of a DG enhancement for triangulated categories. As a consequence we obtain such uniqueness for the unbounded categories of quasi-coherent sheaves, for the triangulated categories of…
This survey is a continuation of the study undertaken in \cite{AS18}. We examine the local structure of Bridgeland moduli spaces $M_\sigma(v,\D)$, where the relevant triangulated category $\D$ is either the bounded derived category…
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…
In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and the triangulated category of singularities of the fiber of W over zero. The main…
A K3 category is by definition a Calabi-Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no…
Achar has recently introduced a family of t-structures on the derived category of equivariant coherent sheaves on a $G$-scheme, generalizing the perverse coherent t-structures of Bezrukavnikov and Deligne. They are called \emph{staggered}…
This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the…
For a given stability condition $\sigma$ on a triangulated category we define a $\sigma$-exceptional collection as an Ext-exceptional collection, whose elements are $\sigma$-semistable with phases contained in an open interval of length…
We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.
We study degenerations of complex projective spaces $\mathbb P^n$ into normal projective klt varieties $X$. If the tangent sheaf of $X$ is semi-stable, we show that $X$ itself is a projective space. If $X$ is a threefold with canonical…