We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations—the generalised Monge–Ampère 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–Ampère 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.

中文翻译：

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Quillen 度量和扰动方程

我们提出了三组不同方程组的无限维前量子线丛和矩图解释——广义 Monge-Ampère 方程、近 Hitchin 系统和 Calabi-Yang-Mills 方程。这些都是已经存在的方程的扰动。我们对广义 Monge-Ampère 方程的构造以代数几何的猜想为条件。此外，我们证明了对于较小的扰动参数值，其中一些方程有解。