Vortex equations in abelian gauged sigma-models

We consider nonlinear gauged sigma-models with Kahler domain and target. For a special choice of potential these models admit Bogomolny (or self-duality) equations -- the so-called vortex equations. We find the moduli space and energy spectrum of the solutions of these equations when the gauge group is a torus T^n, the domain is compact, and the target is C^n or CP^n. We also obtain a large family of solutions when the target is a compact Kahler toric manifold.