Hyper-holomorphic connections on vector bundles on hyper-K\"ahler manifolds

Abstract

We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-K\"ahler manifolds of arbitrary dimension. We describe the DG Lie algebra controlling this deformation problem, and prove that it is formal when the connection is hyper-holomorphic. Moreover, we prove associative formality for derived endomorphisms of a holomorphic vector bundle admitting a projectively hyper-holomorphic connection.Comment: 26 pages. Comments are very welcome