Related papers: Fourier-Mukai transform on abelian surfaces

Due to a theorem by Orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of Fourier-Mukai type. We extend this result to the case of bounded derived categories…

In general, if M is a moduli space of stable sheaves on X, there is a unique alpha in the Brauer group of M such that a pi_M^* alpha^{-1}-twisted universal sheaf exists on X times M. In this paper we study the situation when X and M are K3…

We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a $(d_1,d_2)$-polarized abelian surface, we show how the…

Let $A$ be an abelian variety over a field. The homogeneous (or translation-invariant) vector bundles over $A$ form an abelian category ${\rm HVec}_A$; the Fourier-Mukai transform yields an equivalence of ${\rm HVec}_A$ with the category of…

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…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.

We prove that a bounded complex of coherent sheaves on an abelian variety A, whose Fourier-Mukai transform has support of dimension at most 1, extends to a perfect complex on the standard NC-smooth thickening of A and on the deformation…

We give an explicit description of the Godeaux surfaces that admit an involution such that the quotient surface is birational to an Enriques surface; these surfaces give a 6-dimensional unirational irreducible subset of the moduli space of…

The main result of this paper is a characterization of the abelian varieties $B/K$ defined over Galois number fields with the property that the zeta function $L(B/K;s)$ is equivalent to the product of zeta functions of non-CM newforms for…

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…

Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an O^* gerbe over a genus one fibration which is a…

In this paper we consider moduli spaces of coherent systems on an elliptic curve. We compute their Hodge polynomials and determine their birational types in some cases. Moreover we prove that certain moduli spaces of coherent systems are…

We study the interaction between Fourier-Mukai transforms and perverse filtrations for a certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the "Perverse $\supset$ Chern" phenomenon for these…

We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a…

We study the birational geometry of moduli spaces of semistable sheaves on the projective plane via Bridgeland stability conditions. We show that the entire MMP of their moduli spaces can be run via wall-crossing. Via a description of the…

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…

Kodaira fibred surfaces are a remarkable example of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is…

We modify the standard perfect symmetric obstruction theory for moduli spaces of simple perfect complexes, to the situation of complexes on abelian threefolds with fixed determinant and Fourier-Mukai determinant. As outcome we attach…

Let $K$ be an imaginary quadratic field. Modular forms for GL(2) over $K$ are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over…