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 $M^{\mathrm{nilp}}_{\mathrm{Dol}}(\bar{X}, D)$ of logarithmic Higgs bundles with nilpotent residues and the moduli space $M^{\mathrm{nilp}}_{\mathrm{DR}}(\bar{X}, D)$ of logarithmic connections with nilpotent residues. In this note, we argue that the map is a homeomorphism.