{
  "abstract": "Let $Y$ be a smooth projective threefold with $H^2(Y, \\mathcal{O}_Y)=0$ and unobstructed deformations. We define reflection groups $W_Y^{sm}$ and $W_Y^{big}$ canonically associated to $Y$, acting on the nef, resp. movable cone of a very general deformation of $Y$. If $-K_Y$ is nef, we show that $\\mathrm{Nef}(Y)\\cap\\mathrm{Big}(Y)$ (resp. $\\overline{\\mathrm{Mov}}(Y)\\cap\\mathrm{Big}(Y)$) is a fundamental domain for the action of the corresponding group on the big part of the generic cone. This generalizes work of Wilson and Lutz on Calabi--Yau threefolds. The group $W_Y^{big}$ recovers and gives a deformation-theoretic explanation for the Weyl group action on divisor classes of point blowups of $\\mathbb P^3$ studied by Dolgachev--Ortland and Mukai.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32450",
  "author_total": 1,
  "authors": [
    {
      "name": "Wendelin Lutz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3vj36d9nwcdn4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32450",
  "fulltext_url": null,
  "id": "3vj36d9nwcdn4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32450",
  "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": "W7223703479",
  "pdf_url": "https://arxiv.org/pdf/2610.32450",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3vj36d9nwcdn4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32450",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32450"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Reflection groups on smooth projective threefolds",
  "title_text": "Reflection groups on smooth projective threefolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/3vj36d9nwcdn4",
  "venue": "arXiv",
  "versions": []
}