{
  "abstract": "We give a necessary and sufficient homological criterion for smoothing projective Calabi-Yau threefolds with nodes and anticanonical cones over smooth del Pezzo surfaces of degrees five, six and seven, or over a smooth quadric surface. For some choice of local smoothing components, the criterion requires a relation on a crepant resolution among link classes whose associated local parameters avoid every discriminant. The complexified relation space describes first-order deformations modulo locally trivial ones. Necessity follows from local period and vanishing-cycle arguments; sufficiency applies Friedman's unobstructedness theorem to a crepant partial resolution. Whenever the criterion holds, the deformation space on the chosen components is smooth. A nonsmoothable example, whose deformation space is reduced with four smooth components, shows why nonvanishing at every singular point is insufficient. We also construct a smoothable Batyrev hypersurface admitting no smoothing induced by proper ambient families obtained from Minkowski decompositions at a single lattice degree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35915",
  "author_total": 1,
  "authors": [
    {
      "name": "Bernd Johannes Wuebben"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qvk09y488h9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35915",
  "fulltext_url": null,
  "id": "1qvk09y488h9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35915",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7224084954",
  "pdf_url": "https://arxiv.org/pdf/2610.35915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qvk09y488h9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Smoothing Calabi-Yau threefolds with nodes and del Pezzo cone points",
  "title_text": "Smoothing Calabi-Yau threefolds with nodes and del Pezzo cone points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1qvk09y488h9p",
  "venue": "arXiv",
  "versions": []
}