Related papers: Decorated sheaves and morphisms in tilted hearts

We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…

Let $X$ be a smooth projective surface with a full strong exceptional sequence $\mathfrak{E}$. Under certain conditions, we describe the moduli spaces of framed sheaves on a line in $X$ via linear data, i.e. by realizing them as principal…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…

We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…

We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane.…

Let S be a smooth projective algebraic surface. Generalizing results of Nakajima and Grojnowski, we construct (under some assumptions) an action of the oscillator algebra associated to the cohomology of S, on the cohomology of the moduli…

Let $A$ be the one point extension of an algebra $B$ by a projective $B$-module. We prove that the extension of a given support $\tau$-tilting $B$-module is a support $\tau$-tilting $A$-module; and, conversely, the restriction of a given…

We study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a…

Cohomology of a compatible family of Lie algebroids defined on a family of transverse manifolds is defined. A sheaf of differential forms on a compatible family of Lie algebroids defined over regular open subsets of a simplicial complex is…

The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…

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…

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli…

Given an automorphism of a smooth complex algebraic curve, there is an induced action on the moduli space of semi-stable rank 2 holomorphic bundles with fixed determinant. We give a complete description of the fixed variety in terms of…

A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…

A sheaf of modules on a site is said to be internally projective if sheaf hom with the module preserves epimorphism. In this note, we give an example showing that internally projective sheaves of abelian groups are not in general stable…

In this article, we deal with properties of the reduced Drinfeld double of the composition subalgebra of the Hall algebra of the category of coherent sheaves on a weighted projective line. This study is motivated by applications in the…

The semi-stable ChowHa of a quiver with stability is defined as an analog of the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups of semi-stable loci in representation varieties of quivers.…

We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah's and Tu's results about semistable sheaves over…

The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface case. Among others, the case of elliptic…

In this paper, we investigate the properties of $A$-coherent and $A$-quasi-coherent sheaves within the framework of algebraic geometry over non-algebraically closed fields. We define an $\mathcal{O}_X$-module to be $A$-coherent (resp.…