  We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.
