  We consider the partition function of beta-gamma systems in curved space of
the type discussed by Nekrasov and Witten. We show how the Koszul resolution
theorem can be applied to the computation of the partition functions and to
characters of these systems and find a prescription to enforce the hypotheses
of the theorem at the path integral level. We illustrate the technique in a few
examples: a simple 2-dimensional target space, the N-dimensional conifold, and
a superconifold. Our method can also be applied to the Pure Spinor constraints
of superstrings.
