Rigid holomorphic rank 2 vector bundles on non-K\"ahler surfaces

TL;DR

This paper classifies rigid rank 2 holomorphic vector bundles on non-Kähler surfaces, focusing on minimal class VII surfaces with higher second Betti number, and explores their geometric properties.

Contribution

It provides a comprehensive description of rigid rank 2 bundles on non-Kähler surfaces, addressing gaps in understanding for minimal class VII surfaces with b2 ≥ 4.

Findings

Classification of rigid rank 2 bundles on non-Kähler surfaces

Identification of cases for minimal class VII surfaces with b2 ≥ 4

Insights into deformation properties of these bundles

Abstract

The interest in rigid vector bundles (with respect to determinant preserving deformations) stems from various sources. From a geometric point of view, non-K\"ahler manifolds are of particular interest with respect to this problem. In this article, a description of the various possible cases of rigid rank 2 bundles on non-K\"ahler surfaces is presented. The largest gap of knowledge is for minimal class VII surfaces with $b_{2}(X)\ge 4$.