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

TL;DR

This paper proves that the set of irregular bundles within the moduli space of stable bundles on a Hopf surface is meager, indicating their scarcity.

Contribution

It establishes that irregular bundles form a meager subset in the moduli space of stable bundles on Hopf surfaces, highlighting their rarity.

Findings

Irregular bundles are a meager subset of the moduli space.

The moduli space of stable bundles on Hopf surfaces contains few irregular bundles.

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.