Related papers: Generalized Bogomolov-Gieseker type inequalities o…
We show that the construction of Bayer, Bertram, Macri and Toda gives rise to a Bridgeland stability condition on a principally polarized abelian threefold with Picard rank one by establishing their conjectural generalized…
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…
We investigate the stronger form of the Bogomolov-Gieseker inequality on smooth hypersurfaces in the projective space of any degree and dimension. The main technical tool is the theory of tilt-stability conditions in the derived category.
In this paper, we prove a stronger form of the Bogomolov-Gieseker (BG) inequality for stable sheaves on two classes of Calabi-Yau threefolds, namely, weighted hypersurfaces inside the weighted projective spaces $\mathbb{P}(1, 1, 1, 1, 2)$…
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 investigate the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters constructed by Bridgeland. For a stable sheaf, we give effective bounds of these…
We study the Clifford type inequality for a particular type of curves $C_{2,2,5}$, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable…
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the…
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 a new version of Bogomolov's inequality on normal proper surfaces. This allows to construct Bridgeland's stability condition on such surfaces. In particular, this gives the first known examples of stability conditions on…
We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the…
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…
In this article we are mainly concerned with three dimensional compact K\"ahler spaces with log terminal singularities. We establish the orbifold version of the Bogomolov-Gieseker inequality for stable $\mathbb Q$-sheaves.
We prove Bogomolov's inequality for semistable sheaves on product type varieties in arbitrary characteristic. This gives the first examples of varieties with positive Kodaira dimension in positive characteristic on which Bogomolov's…
We show the existence of Gepner type Bridgeland stability conditions on the triangulated categories of graded matrix factorizations associated with homogeneous polynomials which define general cubic fourfolds containing a plane. The key…
We present a generalization of the Bogomolov-Miyaoka-Yau inequality to Deligne-Mumford surfaces of general type.
Let $S$ be a smooth projective surface on a smooth threefold $X$ such that $X$ has Picard rank 1 and NS$(S)$ is generated by the restriction of divisors from X. We show that if $X$ satisfies the Bogomolov-Gieseker type inequality for tilt…
We generalise Bogomolov's inequality to all coherent torsion-free sheaves on a smooth projective surface.
This article is based on a talk given at the Kinosaki Symposium on Algebraic Geometry in 2015, about a work in progress. We describe a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. We explicitly…
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…