Hyper-holomorphic connections on vector bundles on hyper-K\"ahler manifolds
Algebraic Geometry
2022-07-27 v2
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.
Cite
@article{arxiv.2204.04075,
title = {Hyper-holomorphic connections on vector bundles on hyper-K\"ahler manifolds},
author = {Francesco Meazzini and Claudio Onorati},
journal= {arXiv preprint arXiv:2204.04075},
year = {2022}
}
Comments
26 pages. Version 2: exposition improved, some changes to Sections 3 and 5, geometric applications to projectively hyper-holomorphic vector bundles unchanged