  The one-loop quantum corrections to the mass and central charge of the N=2
vortex in 2+1 dimensions are determined using supersymmetry-preserving
dimensional regularization by dimensional reduction of the corresponding N=1
model with Fayet-Iliopoulos term in 3+1 dimensions. Both the mass and the
central charge turn out to have nonvanishing one-loop corrections which however
are equal and thus saturate the Bogomolnyi bound. We explain BPS saturation by
standard multiplet shortening arguments, correcting a previous claim in the
literature postulating the presence of a second degenerate short multiplet at
the quantum level.
