This brief survey aims to set the stage and summarize some of the ideas under discussion at
the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the …

To every singular reduced projective curve $ X $ one can associate many fine compactified
Jacobians, depending on the choice of a polarization on $ X $, each of which yields a …

We show that for many moduli spaces of torsion sheaves on K3 surfaces, the functor
induced by the universal sheaf is a-functor, hence can be used to construct an …

To every singular reduced projective curve X one can associate, following Esteves, many
fine compactified Jacobians, depending on the choice of a polarization on X, each of which …

We study the cohomology of Jacobians and Hilbert schemes of points on reduced and
locally planar curves, which are however allowed to be singular and reducible. We show …

The Dirac–Higgs bundle is a hyperholomorphic bundle over the moduli space of stable
Higgs bundles of coprime rank and degree. We provide an algebraic generalization to the …

Let X be an abelian scheme over a scheme B. The Fourier–Mukai transform gives an
equivalence between the derived category of X and the derived category of the dual abelian …

We construct modular compactifications of the universal Jacobian stack over the moduli
stack of reduced curves with marked points depending on stability parameters obtained out …

We consider two families of branes supported on the singular locus of the moduli space of
Higgs bundles over a smooth projective curve x. On the one hand, a (BBB)-brane Car (L) …

In this article we study the relation between Arinkin's Poincar\'e sheaf on the compactified
Jacobian over an integral nodal curve and the classical Poincar\'e bundle on the Jacobian of …