On the meagerness of the set of irregular bundles on Hopf surfaces

Abstract

Let ${\mathcal{M}}_{r,c}$ denote the moduli space of stable bundles with rank $r$ and second Chern class $c>0$ on a Hopf surface. We prove that the subset of ${\mathcal{M}}_{r,c}$ formed by irregular bundles is meager.

This text supercedes arXiv:2508.19039 with proof of connectedness of the moduli for r=2 obtained without any auxiliary assumption