Related papers: Flips and variation of moduli schemes of sheaves o…

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.

Let $X$ be a complex projective manifold. Fix two ample line bundles $H_0$ and $H_1$ on $X$. It is the aim of this note to study the variation of the moduli spaces of Gieseker semistable sheaves for polarizations lying in the cone spanned…

Sheaves on non-reduced curves can appear in moduli space of 1-dimensional semistable sheaves over a surface, and moduli space of Higgs bundles as well. We estimate the dimension of the stack $\mathbf{M}_{X}(nC,\chi)$ of pure sheaves…

We study the behavior of the Gieseker space of semistable torsion-free sheaves of rank r and fixed c_1, c_2 on a non-singular projective surface as the polarization varies. It is shown that the ample cone admits a locally finite chamber…

Let $X$ be a nonsingular projective surface over an algebraically closed field with characteristic zero, and $H_-$ and $H_+$ ample line bundles on $X$ separated by only one wall of type $(c_1,c_2)$. Suppose the moduli scheme $M(H_-)$ of…

Let X be a projective irreducible smooth algebraic variety. A "fine moduli space" of sheaves on X is a family F of coherent sheaves on X parametrized by an integral variety M such that : F is flat on M; for all distinct points x, y of M the…

When a non-singular complex projective surface $X$ satisfies that $K_X\sim 0$, we shall show that there are only finitely many isomorphic classes as abstract schemes in the set of moduli scheme of $H$-semistable sheaves with fixed Chern…

For complex projective smooth surface $X$, let $M$ be the coarse moduli scheme of rank-two stable sheaves with fixed Chern classes. Grasping the birational structure of $M$, for example its Kodaira dimension, is a fundamental problem.…

Let $H$ and $H'$ be two ample line bundles over a nonsingular projective surface $X$, and $M(H)$ (resp. $M(H')$) the coarse moduli scheme of $H$-semistable (resp. $H'$-semistable) sheaves of fixed type $(r=2,c_1,c_2)$. In a moduli-theoretic…

Given a quasi-projective scheme M over complex numbers equipped with a perfect obstruction theory and a morphism to a nonsingular quasi-projective variety B, we show it is possible to find an affine bundle M'/ M that admits a perfect…

Let X be an irreducible 2n-dimensional holomorphic symplectic manifold. A reflexive sheaf F is very modular, if its Azumaya algebra End(F) deforms with X to every Kahler deformation of X. We show that if F is a slope-stable reflexive sheaf…

Let f: V --> U be a smooth non-isotrivial family of canonically polarized n-dimensional complex manifolds, where U is the complement of a normal crossing divisor S in a projective manifold Y. We show that some symmetric product of the sheaf…

We prove that the "Thaddeus flips" of $L$-twisted sheaves constructed by Matsuki and Wentworth can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of 1-dimensional Gieseker…

The aim of this paper is to determine a bound of the dimension of an irreducible component of the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Let $X$ be a non-singular irreducible complex surface and let $E$ be a…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

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…

The purpose of this article is to study the deformations of smooth surfaces $X$ of general type whose canonical map is a finite, degree 2 morphism onto a minimal rational surface or onto $\mathbf F_1$, embedded in projective space by a very…

Let $X$ be a complex manifold and $L$ be a holomorphic line bundle on $X$. Assume that $L$ is semi-positive, namely $L$ admits a smooth Hermitian metric with semi-positive Chern curvature. Let $Y$ be a compact K\"ahler submanifold of $X$…

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…

We study sheaves E on a smooth projective curve X which are minimal with respect to the property that $h^0(E \otimes L) >0$ for all line bundles L of degree zero. We show that these sheaves define ample divisors D(E) on the Picard torus…