相关论文: Moduli of Bridgeland semistable objects on 3-folds…
The conjectural Bogomolov-Gieseker (BG) type inequality for tilt semistable objects on projective 3-folds was proposed by Bayer, Macri and the author. In this note, we prove our conjecture for slope stable sheaves with the smallest first…
We develop a framework to modify the Bogomolov-Gieseker type inequality conjecture introduced by Bayer-Macri-Toda, in order to construct a family of geometric Bridgeland stability conditions on any smooth projective 3-fold. We show that it…
We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projective 3-folds. We give an equivalent conjecture which needs…
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…
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…
We study a conjectural relationship among Donaldson-Thomas type invariants on Calabi-Yau 3-folds counting torsion sheaves supported on ample divisors, ideal sheaves of curves and Pandharipande-Thomas's stable pairs. The conjecture is a…
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 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…
For each $0<\alpha<\frac{1}{2}$, there exists a Bayer--Lahoz--Macr{\`{\i}}--Stellari inducing Bridgeland stability condition $\sigma(\alpha)$ on a Kuznetsov component $\mathrm{Ku}(Q)$ of the smooth quadric threefold $Q$. We obtain 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…
We give another proof of Le Potier's result and some variants on moduli spaces of semistable sheaves on the projective plane, using the Bridgeland stability conditions. As an application we study the wall-crossing phenomena of the Hilbert…
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…
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…
On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of…
Famous work of Bridgeland and Smith shows that certain moduli spaces of quadratic differentials are isomorphic to spaces of stability conditions on particular 3-Calabi-Yau triangulated categories. This result has subsequently been…
We give a conjectural construction of Bridgeland stability conditions on the derived category of fibred threefolds. The construction depends on a conjectural Bogomolov-Gieseker type inequality for certain stable complexes. It can be…
For $g,n\geq 0$ a 3-dimensional Calabi-Yau $A_\infty$-category $\mathcal C_{g,n}$ is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Stab}(\mathcal C_{g,n})$, is a moduli space of quadratic…
We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are…
We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces. On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a…
A generalized Bogomolov-Gieseker inequality for tilt-stable complexes on a smooth projective threefold was conjectured by Bayer, Toda, and the author. We show that such inequality holds true in general, if it holds true when the…