Related papers: Bridgeland-Stable Moduli Spaces for K-Trivial Surf…
We describe a close relation between wall crossings in the birational geometry of moduli space of Gieseker stable sheaves $M_H(v)$ on $\bb{P}^2$ and mini-wall crossings in the stability manifold $Stab(D^b(\bb{P}^2))$.
In [BM14b], the first author and Macr\`i constructed a family of nef divisors on any moduli space of Bridgeland-stable objects on a smooth projective variety X. In this article, we extend this construction to the setting of any separated…
Let $X$ be a surface with an ADE-singularity and let $\widetilde{X}$ be its crepant resolution. In this paper, we show that there exists a Bridgeland stability condition $\sigma_X$ on ${\rm D}^b(X)$ and a weak stability condition…
Given a birational modification $X \to Y$ of complex projective varieties with fiber dimension 1 and rational singularities, consider the main component of Bridgeland's moduli space $W \to Y$ of perverse point sheaves on $X/Y$. We give…
We prove the Bogomolov-Gieseker type inequality conjectured by Bayer, Macri and Toda for some products of three curves. This gives the first examples of Bridgeland stability conditions on some threefolds of general type. The key ingredients…
In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…
This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand…
Let $\mathcal{T}$ be a $k$-linear triangulated category. The space of Bridgeland stability conditions on $\mathcal{T}$, denoted by $\mathrm{Stab}(\mathcal{T})$, forms a complex manifold. In this paper, we introduce an equivalence relation…
In this paper, we consider moduli spaces of stable sheaves on abelian surfaces. Our main assumption is the primitivity of the associated Mukai vector. We construct many isomorphisms of muduli spaces induced by Fourier-Mukai functor. As an…
We systematically develop Bridgeland's and Bridgeland-Maciocia's techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier-Mukai transform. As an…
We study flips of moduli schemes of stable torsion free sheaves as wall-crossing phenomena of moduli schemes of stable modules over certain finite dimensional algebra. They are described as stratified Grassmann bundles.
We consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macr\`i-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible…
We continue the study of Lagrangian-invariant objects (LI-objects for short) in the derived category $D^b(A)$ of coherent sheaves on an abelian variety, initiated in arXiv:1109.0527. For every element of the complexified ample cone $D_A$ we…
On a Weierstra{\ss} elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted as $Z^l$-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the…
Let $C$ be a smooth irreducible complex projective curve of genus $g \geq 2$ and $M$ the moduli space of stable vector bundles on $C$ of rank $n$ and degree $d$ with $\gcd(n,d)=1$. A generalised Picard sheaf is the direct image on $M$ of…
In this paper, we prove a Clifford type inequality for the curve $X_{2,2,2,4}$, which is the intersection of a quartic and three general quadratics in $\mathbb{P}^5$. We thus prove a stronger Bogomolov-Gieseker inequality for characters of…
We realize explicit symmetries of Bridgeland stability conditions on any abelian threefold given by Fourier-Mukai transforms. In particular, we extend the previous joint work with Maciocia to study the slope and tilt stabilities of sheaves…
We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the…
We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent…
In this paper, we study the moduli spaces $\mathcal{M}_{\delta,c_2}$ of stable rank-2 vector bundles on non-K\" ahler elliptic surfaces, thus giving a classification these bundles; in the case of Hopf and Kodaira surfaces, these moduli…