Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds (2204.04075v2)

Published 8 Apr 2022 in math.AG

Abstract: We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-K\"ahler 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.

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