Related papers: Bridgeland-Stable Moduli Spaces for K-Trivial Surf…

We provide a systematic way of calculating a quiver region associated to a given exceptional collection, which as an application is used to prove that $\mu$-stable sheaves represented by $2$-step complexes are Bridgeland stable. In the…

Categorical resolutions of singularities are a replacement of resolution of singularities within the realm of triangulated categories. They allow the study of the derived category of a singular variety $X$ via a triangulated category that…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper-K\"ahler manifolds. More precisely, (1) we prove that the fixed loci of the natural…

We study Bridgeland moduli spaces of semistable objects of $(-1)$-classes and $(-4)$-classes in the Kuznetsov components on index one prime Fano threefold $X_{4d+2}$ of degree $4d+2$ and index two prime Fano threefold $Y_d$ of degree $d$…

We prove an effective restriction theorem for stable vector bundles $E$ on a smooth projective variety: $E|_D$ is (semi)stable for all irreducible divisors $D \in |kH|$ for all $k$ greater than an explicit constant. As an application, we…

We construct proper good moduli spaces for moduli stacks of Bridgeland semistable orthosymplectic complexes on a complex smooth projective variety, which we propose as a candidate for compactifying moduli spaces of principal bundles for the…

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 study semistable pairs on elliptic K3 surfaces with a section: we construct a family of moduli spaces of pairs, related by wall crossing phenomena, which can be studied to describe the birational correspondence between moduli spaces of…

Families of Bridgeland stability conditions induce families of stability data, wall-crossing structures and scattering diagrams on the motivic Hall algebra. These structures can be transferred to the quantum torus if the stability…

We introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface, there exists a constant C depending only on the rank and…

We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

We define and study a gluing procedure for Bridgeland stability conditions in the situation when a triangulated category has a semiorthogonal decomposition. As an application we construct stability conditions on the derived categories of…

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…

Moduli spaces of sheaves and Hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from Bridgeland stability conditions and derived category methods. In…

We prove that the Gieseker moduli space of stable sheaves on a smooth projective threefold $X$ of Picard rank 1 is separated from the moduli space of PT stable objects by a single wall in the space of Bridgeland stability conditions on $X$,…

Given an action of a finite group $G$ on the derived category of a smooth projective variety $X$ we relate the fixed loci of the induced $G$-action on moduli spaces of stable objects in $D^b(\mathrm{Coh}(X))$ with moduli spaces of stable…

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen--Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological…

We prove that the moduli stack of Bridgeland semistable holomorphic triples over a curve of $g(C)\geq 1$ with a fixed numerical class and phase is an algebraic stack of finite type over $\mathbb{C}$ and admits a proper good moduli space. We…