We study the Coulomb-Higgs duality of N = 2 supersymmetric abelian Chern-Si
mons theories in 2 + 1 dimensions, by compactifying dual pairs on a circle
of radius R and comparing the resulting N = (2;2) theories in 1 + 1 dimensi
ons. Below the compactification scale, the theory on the Higgs branch reduc
es to the non-linear sigma model on a toric manifold. In the dual theory on
the Coulomb branch, the Kaluza-Klein modes generate an infinite tower of c
ontributions to the superpotential. After resummation, in the limit R --> 0
the superpotential becomes that of the Landau-Ginzburg model which is the
two-dimensional mirror of the toric sigma model. We further examine the con
jecture of all-scale three-dimensional mirror symmetry and observe that it
is consistent with mirror symmetry in 1 + 1 dimensions.