4 citations · 8 across the 14 of their papers we have counts for
19 papers
Moduli spaces of generalised tautological bundles on Hilbert schemes
Andreas Krug, Fabian Reede, Ziyu Zhang
We construct new stable vector bundles on Hilbert schemes of points on algebraic surfaces, which are parametrised by connected components of their moduli spaces. This work generali…
A smooth but non-symplectic moduli of sheaves on a hyperkähler variety
Andreas Krug, Fabian Reede, Ziyu Zhang
For an abelian surface , we consider stable vector bundles on a generalized Kummer variety with . We prove that the connected component of the moduli space which c…
Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds
Fabian Reede
Let be an Enriques surface. Using Beauville's result about the triviality of the Brauer map of , we define a new involution on the category of coherent sheaves on the canoni…
Descent of tautological sheaves from Hilbert schemes to Enriques manifolds
Fabian Reede
Let be a K3 surface which doubly covers an Enriques surface . If is an odd number, then the Hilbert scheme of -points admits a natural quotient…
Stability and certain -functors
Fabian Reede
Let be a K3 surface. We prove that Addington's -functor between the derived categories of and the Hilbert scheme of points maps stable vector bundle…
Picard schemes of noncommutative bielliptic surfaces
Fabian Reede
We study the nontrivial elements in the Brauer group of a bielliptic surface and show that they can be realized as Azumaya algebras with a simple structure at the generic point of…
Smooth components on special iterated Hilbert schemes
Fabian Reede
Let be a smooth projective surface with . We show how to use derived categorical methods to study the geometry of certain special iterated Hilbert schemes associated t…
Stable vector bundles on generalized Kummer varieties
Fabian Reede, Ziyu Zhang
For an abelian surface , we explicitly construct two new families of stable vector bundles on the generalized Kummer variety for . The first is the family…
Stability of some vector bundles on Hilbert schemes of points on K3 surfaces
Fabian Reede, Ziyu Zhang
Let be a projective K3 surfaces. In two examples where there exists a fine moduli space of stable vector bundles on , isomorphic to a Hilbert scheme of points, we prove…
The Fourier-Mukai transform of a universal family of stable vector bundles
Fabian Reede
In this note we prove that the Fourier-Mukai transform induced by the universal family of the moduli space is not fully faithf…
Rank one sheaves over quaternion algebras on Enriques surfaces
Fabian Reede
Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra A on X. Then we study the moduli scheme of torsion free A…
A birational Torelli theorem with a Brauer class
Norbert Hoffmann, Fabian Reede
Let denote the coarse moduli space of semistable vector bundles of rank with trivial determinant over a smooth projective cur…
The cubo-cubic transformation and K3 surfaces
Fabian Reede
In this note we observe that the Cremona transformation in Oguiso's example of Cremona isomorphic but not projectively equivalent quartic K3 surfaces in three-dimensional projectiv…
Examples of smooth components of moduli spaces of stable sheaves
Fabian Reede, Ziyu Zhang
Let M be a projective fine moduli space of stable sheaves on a smooth projective variety X with a universal family E. We prove that in four examples, E can be realized as a complet…
Hermitian Azumaya modules and arithmetic Chern classes
Fabian Reede
We compute arithmetic Chern classes of sheaves on an arithmetic surface X associated to a Hermitian Azumaya algebra.
Torsion-free rank one sheaves over del Pezzo orders
Norbert Hoffmann, Fabian Reede
Let A be a del Pezzo order on the projective plane over the field of complex numbers. We prove that every torsion-free A-module of rank one can be deformed into a locally free A-mo…
The symplectic structure on the moduli space of line bundles on a noncommutative Azumaya surface
Fabian Reede
In this note we prove that the moduli space of torsion-free modules of rank one over an Azumaya algebra on a K3-surface is an irreducible symplectic variety deformation equivalent…
A Deligne pairing for Hermitian Azumaya modules
Fabian Reede
In this short note we want to give a definition of a generalized Deligne pairing for modules over an Azumaya algebra on an arithmetic surface . We do this by defining Hermitian…
Vector bundles and Arakelov geometry on the projective line over the integers
Fabian Reede
We study locally free sheaves of rank two on the projective line over the integers, especially indecomposable ones. Subsequently we apply various concepts of Arakelov geometry to t…