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.
Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds / Meazzini, Francesco; Onorati, Claudio. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 303:1(2023). [10.1007/s00209-022-03176-4]
Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds
Meazzini, Francesco
;Onorati, Claudio
2023
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.File allegati a questo prodotto
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