{
  "abstract": "We present a gluing construction for a class of 6th order geometric non-linear PDE's on a Kähler manifold or orbifold, arising in the study of Bismut Hermitian Einstein complex $3$-folds, the supersymmetric supergravity models in physics, and in Dervan's Z-critical Kähler metrics. As applications, we obtain a desingularization theorem for orbifolds with crepant singularities admitting a solution of the PDE, as well as a blowing-up of points theorem for smooth complex $3$-folds admitting such solutions. These results yield new examples of regular Bismut Hermitian Einstein structures on the smooth manifolds $3(S^2\\times S^4)\\sharp 4(S^3\\times S^3)$, $5(S^2\\times S^4)\\sharp 6(S^3\\times S^3)$ and $S^1\\times 9(S^2\\times S^3)$, as well as infinite topological types of smooth compact $7$-dimensional manifolds $Y_7$, providing new solutions to the supersymmetric ${\\rm AdS}_3 \\times Y_7$ type IIB and ${\\rm AdS}_2 \\times T^2 \\times Y^7$ type $D=11$ supergravity models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25250",
  "author_total": 4,
  "authors": [
    {
      "name": "Vestislav Apostolov"
    },
    {
      "name": "Abdellah Lahdili"
    },
    {
      "name": "Kuan-Hui Lee"
    },
    {
      "name": "Frédéric Rochon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avcypywwwfz23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25250",
  "fulltext_url": null,
  "id": "avcypywwwfz23",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25250",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214113942",
  "pdf_url": "https://arxiv.org/pdf/2609.25250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avcypywwwfz23.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.25250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A gluing construction of $Z$-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds",
  "title_text": "A gluing construction of Z-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/avcypywwwfz23",
  "venue": "arXiv",
  "versions": []
}