Abstract
We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equationsâ��the generalised Mongeâ��AmpA¨re equation, the almost Hitchin system, and the Calabiâ��Yangâ��Mills equations. These are all perturbations of already existing equations. Our construction for the generalised Mongeâ��AmpA¨re 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.
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