Vector bundles on blown-up Hopf surfaces

TL;DR

This paper investigates the structure of moduli spaces of vector bundles on blown-up primary Hopf surfaces, revealing that some of these spaces lack compact components, which impacts the classification of certain complex surfaces.

Contribution

It demonstrates that specific moduli spaces of vector bundles on blown-up Hopf surfaces have no compact components, providing new insights into the geometry of class VII surfaces.

Findings

Certain moduli spaces lack compact components

Implications for classification of class VII surfaces

Advances understanding of vector bundles on Hopf surfaces

Abstract

We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class $VII$ surfaces.