Related papers: Orbifold Bogomolov-Gieseker inequalities on compac…

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.

Assume that $X$ is a compact complex analytic variety which has quotient singularities in codimension 2, and that $\mathcal{F}$ is a reflexive sheaf on $X$. Using orbifold modifications, we can define first and second homological Chern…

In this article, we prove the orbifold version of the Bogomolov-Gieseker inequality for stable $\mathbb Q$-sheaves on K\"ahler varieties, generalizing our earlier work \cite{GP25} in dimension three. We also provide a characterization of…

In this paper, we study semistable Higgs sheaves over compact K\"ahler manifolds, we prove that there is an approximate admissible Hermitian-Einstein structure on a semi-stable reflexive Higgs sheaf and consequently, the Bogomolove type…

We prove that if $X$ is a compact complex analytic variety, which has quotient singularities in codimension 2, then there is a projective bimeromorphic morphism $f\colon Y\to X$, such that $Y$ has quotient singularities, and that the…

In this paper, we obtain the generalized Bogomolov inequality for reflexive Higgs sheaves defined on the regular locus of compact K\"ahler klt spaces. As an application, we establish the Miyaoka-Yau inequality for all minimal K\"ahler klt…

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 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 establish a stronger Bogomolov--Gieseker type inequality for slope-semistable sheaves on the smooth quintic threefold. Our approach combines a refined restriction theorem for tilt-stable objects with explicit Clifford-type bounds for…

We propose a conjectural stronger version of Bogomolov-Gieseker inequality for stable sheaves on quintic 3-folds. Our conjecture is derived from an attempt to construct a Bridgeland stability condition on graded matrix factorizations, which…

We prove a Bogomolov-Gieseker type inequality for the third Chern characters of stable sheaves on Calabi-Yau 3-folds and a large class of Fano 3-folds with given rank and first and second Chern classes. The proof uses the spreading-out…

An orbifold version of Bogomolov decomposition theorem is established for compact K\"ahler spaces with quotient singularities and first Chern class zero.The proof is a direct adaptation of the classical smooth case, using Ricci-flat…

In this note, we prove the Bogomolov's inequality over a reduced, compact, irreducible, K\"ahler complex space that is smooth in codimension 2. The proof is obtained by a reduction to the smooth case, using Hironaka's resolution of…

Let $X$ be a normal compact K\"ahler variety, and $\mathcal{F}$ a coherent reflexive sheaf on $X$. We investigate the existence of admissible Hermitian metrics on $\mathcal{F}$. If moreover $\mathcal{F}$ is slope stable, we also study the…

In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact K\"ahler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact…

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 prove a version of the Bogomolov-Gieseker inequality on smooth projective surfaces of general type in positive characteristic, which is stronger than the result by Langer when the ranks of vector bundles are sufficiently large. Our…

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 $\mathbb{P}(1, 1, 1, 1, 2)$…

We prove new Sobolev type inequalities on compact K\"ahler manifolds with positive Ricci curvature. A proof of an already existing Sobolev inequality in the classical Bidaut-V\'eron and V\'eron approach is also discussed.

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…