Quillen metrics and perturbed equations

Abstract

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.

arXiv commentChanged the statement of theorem 1.2 to exclude the Gieseker-Higgs stable case because the proof is incorrect. Also corrected other typographical errors