{
  "abstract": "We study well-formed weighted projective threefolds $X=\\mathbb P(w_0,w_1,w_2,w_3)$ that admit a $\\mathbb Q$-Gorenstein smoothing to a smooth Fano threefold of Picard number one. For del Pezzo threefolds $V_d$ and prime Fano threefolds $Y_g$, we derive three necessary numerical and local conditions: the anticanonical volume equation, an identity obtained from the linear term of the anticanonical Hilbert polynomial, and a global section condition for smoothing the transversal $A$-singularities along coordinate curves. A computer search using these conditions determines all numerical candidates, apart from the known infinite family for $V_5$, with $w_0+w_1+w_2+w_3\\leq 5000$. We construct $\\mathbb Q$-Gorenstein smoothings to $V_1, V_2, Y_6, Y_{10},$ and $Y_{12}$ from numerical candidates of weighted projective threefolds, and prove that $\\mathbb P(2,5,8,25)$, although a numerical candidate for $V_4$, is not $\\mathbb Q$-Gorenstein smoothable. To identify the smooth fibers, we also give a vanishing-cycle criterion ensuring that Picard number one is preserved under the smoothing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37268",
  "author_total": 2,
  "authors": [
    {
      "name": "Jungkai Alfred Chen"
    },
    {
      "name": "Yongnam Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9sttrw58zt584.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37268",
  "fulltext_url": null,
  "id": "9sttrw58zt584",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37268",
  "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": "W7214972583",
  "pdf_url": "https://arxiv.org/pdf/2609.37268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9sttrw58zt584.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weighted projective spaces admitting $\\mathbb Q$-Gorenstein smoothings to Fano threefolds with Picard number one",
  "title_text": "Weighted projective spaces admitting ℚ-Gorenstein smoothings to Fano threefolds with Picard number one",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/9sttrw58zt584",
  "venue": "arXiv",
  "versions": []
}