On the nilpotent residue non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties

Abstract

In arXiv:2408.16441, the authors proved that on a projective log smooth variety $(\bar{X},D)$ there is a continuous bijection between the moduli space $M_{\mathrm{Dol}}^{\mathrm{nilp}}(\bar{X},D)$ of logarithmic Higgs bundles with nilpotent residues and the moduli space $M_{\mathrm{DR}}^{\mathrm{nilp}}(\bar{X},D)$ of logarithmic connections with nilpotent residues. In this note, we argue that the map is a homeomorphism.