{
  "abstract": "We study well-formed weighted projective threefolds that admit $\\mathbb Q$-Gorenstein smoothings to $\\mathbb P^3$. Two families are known: the $\\mathbb P^2$-type and the $Q$-type, and it is conjectured that these are the only possibilities. We derive numerical and local necessary conditions for such a smoothing. In addition to the anticanonical volume equation, constancy of the anticanonical Hilbert polynomial yields a further identity when all codimension two singularities are of $A$-type. We also obtain a semigroup condition governing the existence of global smoothing directions along codimension two curves with transverse $A$-type singularities. We apply these conditions to prove the expected classification in several cases. In particular, for every fixed square-free integer $d$, there are only finitely many $\\mathbb Q$-Gorenstein smoothable spaces $\\mathbb P(1,a,b,c)$ such that $\\gcd(a,b)=d$. Our method reduces the possible weights to a finite exact computation; for every prime $p\\le100$, the computation produces only members of the two expected families. Finally, we prove the classification when $\\gcd(a,b)=d$ and $a=d^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37242",
  "author_total": 2,
  "authors": [
    {
      "name": "Jungkai Alfred Chen"
    },
    {
      "name": "Yongnam Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8mzme702nzsc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37242",
  "fulltext_url": null,
  "id": "a8mzme702nzsc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37242",
  "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": "W7214949640",
  "pdf_url": "https://arxiv.org/pdf/2609.37242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8mzme702nzsc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weighted projective spaces admitting $\\mathbb Q$-Gorenstein smoothings to $\\mathbb P^3$",
  "title_text": "Weighted projective spaces admitting ℚ-Gorenstein smoothings to ℙ^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/a8mzme702nzsc",
  "venue": "arXiv",
  "versions": []
}