Rigid holomorphic rank 2 vector bundles on non-Kähler surfaces

2011/04/13 by Kühnel, Marco
#14J60 #32G13 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1104.2489

Abstract

The interest in rigid vector bundles (with respect to determinant preserving deformations) stems from various sources. From a geometric point of view, non-Kähler 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-Kähler surfaces is presented. The largest gap of knowledge is for minimal class VII surfaces with b₂(X)≥ 4.

Related

• Holomorphic vector bundles on non-algebraic surfaces
• Holomorphic rank-2 vector bundles on non-Kahler elliptic surfaces
• Stable bundles on non-Kahler elliptic surfaces
• Examples of non-rigid, modular vector bundles on hyperkähler manifolds
• On the existence of Ulrich vector bundles on some irregular surfaces