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

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 endom...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2023, Vol.303 (1), Article 17
Main Authors: Meazzini, Francesco, Onorati, Claudio
Format: Article
Language:English
Subjects:
Deformation
Lie groups
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-022-03176-4