  Let $K\to U(V)$ be a unitary representation of the compact Lie group $K$.
Then there is a canonical moment mapping $\rho\colon V\to\mathfrak k^*$. We
have the Koszul complex ${\mathcal K}(\rho,\mathcal C^\infty(V))$ of the
component functions $\rho_1,...,\rho_k$ of $\rho$. Let $G=K_{\mathbb C}$, the
complexification of $K$. We show that the Koszul complex is a resolution of the
smooth functions on $\rho^{-1}(0)$ if and only if $G\to\GL(V)$ is 1-large, a
concept introduced in earlier work of the second author. Now let $M$ be a
symplectic manifold with a Hamiltonian action of $K$. Let $\rho$ be a moment
mapping and consider the Koszul complex given by the component functions of
$\rho$. We show that the Koszul complex is a resolution of the smooth functions
on $Z=\rho^{-1}(0)$ if and only if the complexification of each symplectic
slice representation at a point of $Z$ is 1-large.
