Related papers: Sheaves on abelian surfaces and Strange Duality

In this paper we give a lower bound for the codimension of the Andreotti-Mayer loci in the moduli space of principally polarized complex abelian varieties. We also present a conjecture on this codimension.

Let $X$ be a finite connected simplicial complex, and let $\delta$ be a perversity (i.e., some function from integers to integers). One can consider two categories: (1) the category of perverse sheaves cohomologically constructible with…

We generalise the proof by Marian and Oprea of rank-level duality for non-abelian theta functions to the case of sections of line bundles (conformal blocks) over moduli spaces of parabolic vector bundles over a projective smooth curve. We…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

To every oriented tree, we associate a moduli problem for sheaves over a projective manifold $X$. We define the corresponding notion of semistability and establish the existence of moduli spaces. Applying the results to the tree *->*, we…

The aim of this paper is to prove the existence of large complete subvarieties in moduli spaces of rank two stable sheaves with arbitrary $c_1$ and sufficiently large $c_2$ on algebraic surfaces. Then we study the restriction of these…

We discuss and extend some of the results obtained in "Arakelov inequalities and the uniformization of certain rigid Shimura varieties" (math.AG/0503339), restricting ourselves to the two dimensional case, i.e. to surfaces Y mapping…

We study the Albanese image of a compact K\"ahler manifold whose geometric genus is one. We prove that if the Albanese map is not surjective, then the manifold maps surjectively onto an ample divisor in some abelian variety, and in many…

The theory of $\Theta$-stratifications generalizes a classical stratification of the moduli of vector bundles on a smooth curve, the Harder-Narasimhan-Shatz stratification, to any moduli problem that can be represented by an algebraic…

The present article studies decompositions of vector bundles on the moduli stack of elliptic curves that are pushforwards of vector bundles on moduli of elliptic curves with level structure. These imply decomposition results for rings of…

We study the moduli space of Gieseker semi-stable sheaves on the complex projective plane supported on sextic curves and having Euler characteristic one. We determine locally free resolutions of length one for all such sheaves. We decompose…

We study the duality of moduli of k- and (n-k)-dimensional slices of euclidean n-cubes, and establish the optimal upper bound 1.

We study projective models of generalized Kummer fourfolds via O'Grady's theta groups and the classical Coble cubic. More precisely, we establish a duality between two singular models of the generalized Kummer fourfold of a Jacobian abelian…

This is the sequel to arXiv:math/0001089. In this paper, we complete the promised description of moduli of abelian surfaces of low degree, covering the cases of degree (1,12), (1,14), (1,16), (1,18) and (1,20). In each case, we describe…

We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two…

We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the…

We show that the Fourier-Mukai transfortm on an abelian surface induces a birational map of the moduli space of stablke sheaves.

This article investigates why the genus two, supermoduli space of curves will split in contrast to, potentially, almost all other supermoduli spaces. We use that the dimension of the odd, versal deformation space of a genus two, super…

Periods of moduli spaces of stable sheaves on K3 surfaces were computed by Mukai, O'Grady and the author. In this paper, we shall treat moduli spaces of stable sheaves on abelian surfaces.

Fujita's second theorem for K\"ahler fibre spaces over a curve asserts that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. We focus on our…