English

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.

Keywords

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

R2 v1 2026-06-22T18:08:45.554Z