{
  "id": "2204.04075",
  "version": "v1",
  "published": "2022-04-08T13:50:53.000Z",
  "updated": "2022-04-08T13:50:53.000Z",
  "title": "Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds",
  "authors": [
    "Francesco Meazzini",
    "Claudio Onorati"
  ],
  "comment": "26 pages. Comments are very welcome!",
  "categories": [
    "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. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-08T13:50:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J42",
      "32G07",
      "14D15"
    ],
    "keywords": [
      "hyper-kähler manifolds",
      "complex vector bundles",
      "study infinitesimal deformations",
      "holomorphic vector bundle admitting",
      "arbitrary dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}