The Journal of Geometric Analysis | 2019
Solutions to Donaldson’s Hyperkähler Reduction on a Curve
Abstract
We study an infinite-dimensional hyperkähler reduction introduced by Donaldson and associated with the constant scalar curvature equation on a Riemann surface. It is known that the corresponding moment map equations admit special solutions constructed from holomorphic quadratic differentials. Here we obtain a more general existence result and so a larger hyperkähler moduli space.