Following the identically named paper by Donaldson from 2000, the mapping space from a smooth manifold into a suitable target classifies geometric structures on the domain. To obtain a moduli space for these structures, it is necessary to quotient out symmetries, which can be done by a Kähler reduction. This talk will introduce the required techniques for this procedure. We will equip the mapping space with a Kähler structure, extend a group action from the domain to the mapping space and show that it is Hamiltonian. Hence we can construct a moment map and perform the desired reduction.

As an example of this method, we will see how LS-graphs in the cotangent bundle of a complex manifold can be identified with Kähler potentials modulo constants.