{
  "abstract": "We show that the fundamental group is not locally stable under non-collapsed Gromov--Hausdorff convergence, even among closed Ricci-flat Kähler four-manifolds. More precisely, we construct families of Ricci-flat Kähler metrics on $K3$ surfaces and Enriques surfaces that converge to the same compact flat orbifold. Using the same mechanism, we further construct two families of closed locally hyperkähler Ricci-flat four-manifolds, with fundamental groups $\\mathbb Z_2$ and $\\mathbb Z_2\\times\\mathbb Z_2$, respectively, which converge to the same compact flat orbifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05795",
  "author_total": 2,
  "authors": [
    {
      "name": "Alejandro Bellati"
    },
    {
      "name": "Ignacio Bustamante"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q8p2cr04cqkf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05795",
  "fulltext_url": null,
  "id": "3q8p2cr04cqkf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05795",
  "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": "W7220729812",
  "pdf_url": "https://arxiv.org/pdf/2610.05795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q8p2cr04cqkf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Instability of the Fundamental Group for Ricci-Flat Kähler 4-Manifolds",
  "title_text": "Instability of the Fundamental Group for Ricci-Flat Kähler 4-Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3q8p2cr04cqkf",
  "venue": "arXiv",
  "versions": []
}