  We use the framework of Quot schemes to give a novel description of the
moduli spaces of stable n-pairs, also interpreted as gauged vortices on a
closed Riemann surface with target Mat(r x n, C), where n >= r. We then show
that these moduli spaces embed canonically into certain Grassmann manifolds,
and thus obtain natural Kaehler metrics of Fubini-Study type; these spaces are
smooth at least in the local case r=n. For abelian local vortices we prove
that, if a certain "quantization" condition is satisfied, the embedding can be
chosen in such a way that the induced Fubini-Study structure realizes the
Kaehler class of the usual L^2 metric of gauged vortices.
