  An Abelian gauge theory with Chern-Simons term is investigated for a
four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex
function is employed to modify the rainbow-ladder approximation for the
Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show
the gauge dependence for the resulting phase boundary for the parity and the
chiral symmetry.
