  We come up with infinite-dimensional prequantum line bundles and moment map
interpretations of three different sets of equations - the generalised
Monge-Amp`ere equation, the almost Hitchin system, and the Calabi-Yang-Mills
equations. These are all perturbations of already existing equations. Our
construction for the generalised Monge-Amp`ere equation is conditioned on a
conjecture from algebraic geometry. In addition, we prove that for small values
of the perturbation parameters, some of these equations have solutions.
