  Taking (2+1)-dimensional pure Einstein gravity for arbitrary genus $g$ as a
model, we investigate the relation between the partition function formally
defined on the entire phase space and the one written in terms of the reduced
phase space. In particular the case of $g=1$ is analyzed in detail.
  By a suitable gauge-fixing, the partition function $Z$ basically reduces to
the partition function defined for the reduced system, whose dynamical
variables are $(\tau^A, p_A)$. [The $\tau^A$'s are the Teichm\"uller
parameters, and the $p_A$'s are their conjugate momenta.]
  As for the case of $g=1$, we find out that $Z$ is also related with another
reduced form, whose dynamical variables are $(\tau^A, p_A)$ and $(V, \sigma)$.
[Here $\sigma$ is a conjugate momentum to 2-volume $V$.] A nontrivial factor
appears in the measure in terms of this type of reduced form. The factor turns
out to be a Faddeev-Popov determinant coming from the time-reparameterization
invariance inherent in this type of formulation. Thus the relation between two
reduced forms becomes transparent even in the context of quantum theory.
  Furthermore for $g=1$, a factor coming from the zero-modes of a differential
operator $P_1$ can appear in the path-integral measure in the reduced
representation of $Z$. It depends on the path-integral domain for the shift
vector in $Z$: If it is defined to include $\ker P_1$, the nontrivial factor
does not appear. On the other hand, if the integral domain is defined to
exclude $\ker P_1$, the factor appears in the measure. This factor can depend
on the dynamical variables, typically as a function of $V$, and can influence
the semiclassical dynamics of the (2+1)-dimensional spacetime.
  These results shall be significant from the viewpoint of quantum gravity.
