  We give a simple description of the classical moduli space of vacua for
supersymmetric gauge theories with or without a superpotential. The key
ingredient in our analysis is the observation that the lagrangian is invariant
under the action of the complexified gauge group $\Gc$. From this point of view
the usual $D$-flatness conditions are an artifact of Wess--Zumino gauge. By
using a gauge that preserves $\Gc$ invariance we show that every constant
matter field configuration that extremizes the superpotential is $\Gc$
gauge-equivalent (in a sense that we make precise) to a unique classical
vacuum. This result is used to prove that in the absence of a superpotential
the classical moduli space is the algebraic variety described by the set of all
holomorphic gauge-invariant polynomials. When a superpotential is present, we
show that the classical moduli space is a variety defined by imposing
additional relations on the holomorphic polynomials. Many of these points are
already contained in the existing literature. The main contribution of the
present work is that we give a careful and self-contained treatment of limit
points and singularities.
