  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.
