  Superspace of rank $n$ is a $\mathbb{Q}$-algebra with $n$ commuting
generators $x_1, \dots, x_n$ and $n$ anticommuting generators $\theta_1, \dots,
\theta_n$. We present an extension of the Vandermonde determinant to superspace
which depends on a sequence $\mathbf{a} = (a_1, \dots, a_r)$ of nonnegative
integers of length $r \leq n$. We use superspace Vandermondes to construct
graded representations of the symmetric group. This construction recovers
hook-shaped Tanisaki quotients, the coinvariant ring for the Delta Conjecture
constructed by Haglund, Rhoades, and Shimozono, and a superspace quotient
related to positroids and Chern plethysm constructed by Billey, Rhoades, and
Tewari. We define a notion of partial differentiation with respect to
anticommuting variables to construct doubly graded modules from superspace
Vandermondes. These doubly graded modules carry a natural ring structure which
satisfies a 2-dimensional version of Poincar\'e duality. The application of
polarization operators gives rise to other bigraded modules which give a
conjectural module for the symmetric function $\Delta'_{e_{k-1}} e_n$ appearing
in the Delta Conjecture of Haglund, Remmel, and Wilson.
