Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds

Abstract

We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-Kähler manifolds of arbitrary dimension. In particular, we describe the DG Lie algebra controlling this deformation problem. Moreover, we prove associative formality for derived endomorphisms of a holomorphic vector bundle admitting a projectively hyper-holomorphic connection.

arXiv comment26 pages. Version 2: exposition improved, some changes to Sections 3 and 5, geometric applications to projectively hyper-holomorphic vector bundles unchanged