  Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be
viewed as generalizations or analogues to Yang-Mills connections and, in
particular, Hermitian-Yang-Mills connections. We proved an analytic
compactification of the moduli spaces of vortices and coupled vortices on
hermitian vector bundles over compact K\"ahler manifolds. In doing so we
introduced the concept of ideal coupled vortices and characterized the
singularities of ideal coupled vortices as well as Hermitian-Yang-Mills
connections.
