{
  "abstract": "Let $X$ be a compact log-canonical Kähler $n$-fold, $n\\ge3,$ with trivial canonical sheaf and with isolated singularities. We prove that the generic fibres of a semi-universal deformation of $X$ have Du Bois invariant $b^{1,n-2}=0$ at the singular points. Under a certain topological hypothesis on $X$ the generic fibres have also link invariant $l^{1,n-2}=0.$ If $X$ is a projective log-canonical $n$-fold, $n\\ge3,$ with ample anti-canonical sheaf and with isolated singularities then the generic fibres have $b^{1,n-2}=l^{1,n-2}=0$ (without the topological hypothesis). These are generalizations of recent results of Tenie `Global smoothing of singular Fano and Calabi--Yau varieties' and an older result of Namikawa `Deformation theory of Calabi--Yau threefolds and certain invariants of singularities.'",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00758",
  "author_total": 1,
  "authors": [
    {
      "name": "Yohsuke Imagi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xtw3qxfk01tg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00758",
  "fulltext_url": null,
  "id": "8xtw3qxfk01tg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00758",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7206199667",
  "pdf_url": "https://arxiv.org/pdf/2609.00758",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xtw3qxfk01tg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00758",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00758"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities",
  "title_text": "Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/8xtw3qxfk01tg",
  "venue": "arXiv",
  "versions": []
}