An Analytic Application of Geometric Invariant Theory II: Coarse Moduli Spaces
arXiv:2108.03255 · doi:10.1016/j.geomphys.2022.104467
Abstract
In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact Kähler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in the weakly normal category is a coarse moduli space in the sense of complex geometry when the topology is fixed as induced by the space of Hermite-Einstein connections modulo the group of unitary gauge transformations.
To appear in Journal of Geometry and Physics