Related papers: Rank two sheaves with maximal third Chern characte…

By results of the author there exists a projective (holomorphic) symplectic desingularization of the moduli space of rank-two torsion-free sheaves on a genus-two Jacobian with $c_1=0$ and $c_2=2$. This desingularization has a natural map to…

We consider the singuralities of 2-dimensional moduli spaces of semi-stable sheaves on K3 surfaces. We show that the moduli space is normal, in particular the singuralities are rational double points. We also describe the exceptional locus…

Let $X$ be a projective K3 surface with generic polarization $\cO_X(1)$ and let $M_c=M(2,0,c)$ be the moduli space of semistable torsion-free sheaves on $X$ of rank 2, with Chern classes $c_1=0$ and $c_2=c$. When $c=2n\ge 4$ is even, $M_c$…

We show that certain semistable sheaves on the projective plane with linear Hilbert polynomial are cokernels of semistable morphisms of decomposable sheaves.We exhibit certain locally closed subvarieties of moduli spaces of semistable…

The moduli space $M(c_2)$, of stable rank two vector bundles of degree one on a very general quintic surface $X\subset {\mathbb P}^3$, is irreducible for all $c_2\geq 4$ and empty otherwise.

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…

Let $X$ be a smooth projective curve of genus $g \geq 2$ and $M$ be the moduli space of rank 2 stable vector bundles on $X$ whose determinants are isomorphic to a fixed odd degree line bundle $L$. There has been a lot of works studying the…

We prove Bogomolov type inequalities for high Chern characters of semistable sheaves satisfying certain Frobenius semipositivity. The key ingredients in the proof are a high rank generalization of the asymptotic Riemann-Roch theorem and…

We study semi-stable sheaves of rank $2$ with Chern class $c_1=0$, $c_2=2$ and $c_3=0$ on the Fano 3-folds $V_4$ of Picard number $1$, degree $4$ and index $2$. We show the moduli space of such sheaves is isomorphic to the moduli space of…

Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N; M), on Specs(M) equipped with the dual Zariski topology…

We investigate the moduli space of sheaves supported on space curves of degree 4 and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

The main result of the present paper is a construction of relative moduli spaces of stable sheaves over the stack of quasipolarized projective surfaces. For this, we use the theory of good moduli spaces, whose study was initiated by Alper.…

We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on…

Let X be a general complex Fano threefold of genus 8. We prove that the moduli space of rank two semistable sheaves on X with Chern numbers c_1=1, c_2=6 and c_3=0 is isomorphic to the Fano surface F(X) of conics on X. Inside F(X), the…

We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…

We classify thick irreducible 3-spherical twin buildings of rank at least 3 in which every panel contains at least 6 chambers. Together with the Main result of [11] we obtain a classification of thick irreducible 3-spherical twin buildings.

We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a…

Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…

We study torsion-free, rank 2 Higgs sheaves on genus one fibered surfaces, (semi)stable with respect to suitable polarizations in the sense of Friedman and O'Grady. We prove that slope-semistability of a Higgs sheaf on the surface implies…

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with…