Abelian vortices on Kaehler manifolds

I will consider abelian vortex equations defined on compact Kähler
manifolds of arbitrary dimension. When the manifold is simply
connected or an abelian variety, I shall give an explicit description
of the moduli spaces and explain how to compute the Kähler class and
volume of the natural L^{^2}-metric. I will also recall how vortex moduli
spaces relate to spaces of holomorphic maps from Kähler manifolds to
toric targets.