# Quillen metrics and perturbed equations

## TL;DR

This paper introduces infinite-dimensional prequantum line bundles and moment map frameworks for perturbed geometric equations, establishing solution existence for small perturbations under certain conditions.

## Contribution

It provides a novel geometric interpretation of perturbed equations and proves solution existence in specific cases, extending previous work on unperturbed equations.

## Key findings

- Constructed prequantum line bundles for perturbed equations
- Established moment map interpretations for these equations
- Proved existence of solutions for small perturbations

## 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.