Quillen metrics and perturbed equations
Mathematical Physics
2017-11-21 v2 Algebraic Geometry
Differential Geometry
math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.1702.01057,
title = {Quillen metrics and perturbed equations},
author = {Vamsi Pritham Pingali},
journal= {arXiv preprint arXiv:1702.01057},
year = {2017}
}
Comments
Changed the statement of theorem 1.2 to exclude the Gieseker-Higgs stable case because the proof is incorrect. Also corrected other typographical errors