In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian
surfaces. Our main assumption is the primitivity of the associated Mukai vector. We …

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in
mathematics for at least two centuries. In the last three decades the development of a …

In this paper, we consider the preservation of stability by using the notion of twisted stability.
As applications,(1) we show that moduli spaces of stable sheaves on K3 and abelian …

On a Weierstraß elliptic surface, we describe the action of the relative Fourier-Mukai
transform on the geometric chamber of Stab (X), and in the K3 case we also study the action …

A bstract M5 branes probing D-type singularities give rise to 6d (1, 0) SCFTs with SO× SO
flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor …

On a Weierstra {\ss} elliptic surface $ X $, we define alimit'of Bridgeland stability conditions,
denoted as $ Z^ l $-stability, by moving the polarisation towards the fiber direction in the …

We study doubly-periodic instantons, ie instantons on the product of a 1-dimensional
complex torus T with a complex line ³, with quadratic curvature decay. We determine the …

We give an introductory review of Fourier-Mukai transforms and their application to various
aspects of moduli problems, string theory and mirror symmetry. We develop the necessary …

Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau three-
fold $ X $ is seen to have an expected adiabatic form for its induced cohomology operation …

Let X→ B be an elliptic surface and M (a, b) the moduli space of torsion-free sheaves on X
which are stable of relative degree zero with respect to a polarization of type aH+ bμ, H …