Related papers: Semistable sheaves on Del Pezzo surfaces and Krone…

Let $\clX$ a projective stack over an algebraically closed field $k$ of characteristic 0. Let $\clE$ be a generating sheaf over $\clX$ and $\clO_X(1)$ a polarization of its coarse moduli space $X$. We define a notion of pair which is the…

This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013. Given a collection of $m$ finite factorizable sheaves $\{\CX_k\}$, we construct here some perverse sheaves over configuration spaces of points on a projective line…

In this paper, we study the Picard group of the moduli space of semistable sheaves on a smooth quadric surface. We polarize the surface by an ample divisor close to the anticanonical class. We focus especially on moduli spaces of sheaves of…

The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced…

In this paper, we study the geometric invariant theory on algebraic spaces, and construct te moduli spaces of $\mathcal{H}$-semistable sheaves on projective Deligne-Mumford stacks over algebraic spaces $S$. We prove that this moduli space…

We prove a number of results to the general effect that, under obviously necessary numerical and determinant constraints, "most" morphisms between fixed bundles on a complex elliptic curve produce (co)kernels which can either be specified…

Let X be either a smooth K3 surface or a smooth Fano variety (i.e. $-K_X$ is ample) of dimension $n$ and index $i_X> n-3$ and let E be an initialized Ulrich bundle on X. In this paper, we show that the syzygy bundle $S(E)$, defined as the…

We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…

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 prove the irreducibility of the moduli space of rank 2 semistable torsion free sheaves (with a generic polarization and any value of c_2) on a K3 or a del Pezzo surface. In the case of a K3 surface, we need to prove a result on the…

By proving a particular case of a conjecture of Drezet, we show that a component of the Maruyama scheme of the semi-stable sheaves on the projective space $\PP^n$ of rank n and Chern polynomial $(1+t)^{n+2}$ is isomorphic to the Kronecher…

In this paper, we study the asymptotic behaviors of the Betti numbers and Picard numbers of the moduli space $M_{\beta,\chi}$ of one-dimensional sheaves supported in a curve class $\beta$ on $S$ with Euler characteristic $\chi$. We…

Given a vector bundle $E$ on a complex reduced curve $C$ and a subspace $V$ of $H^0(E)$ which generates $E$, one can consider the kernel of the evaluation map $ev_V:V\otimes \mathcal{O}_C\to E$, i.e. the {\it kernel bundle } $M_{E,V}$…

A ribbon is a non-reduced curve modelled on the first infinitesimal neighbourhood of a smooth curve in a surface. This paper is devoted to describe some properties of coherent sheaves on such a curve and their Simpson moduli space. In…

Moduli spaces of semistable torsion-free sheaves on a K3 surface $X$ are often holomorphic symplectic varieties, deformation equivalent to a Hilbert scheme parametrizing zero-dimensional subschemes of $X$. In fact this should hold whenever…

Using an existence criterion for good moduli spaces of Artin stacks by Alper-Fedorchuk-Smyth we construct a proper moduli space of rank two sheaves with fixed Chern classes on a given complex projective manifold that are…

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S…

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…

The goal of this paper is the study of simple rank 2 parabolic vector bundles over a $2$-punctured elliptic curve $C$. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to $\mathbb{P}^1 \times…

We investigate Hochschild cohomology and homology of admissible subcategories of derived categories of coherent sheaves on smooth projective varieties. We show that the Hochschild cohomology of an admissible subcategory is isomorphic to the…