{
  "abstract": "We show that, for $k\\geq 3$, a lattice in the unitriangular Lie group $U_k(\\mathbb{R})$ is the fundamental group of a smooth quasi-projective complex algebraic variety if and only if $k=3$. The proof uses the conjugation symmetry and weight conditions of mixed Hodge structure on the Malcev Lie algebra proven by Morgan. This result identifies a family of groups that must be excluded in the search for smooth quasi-projective varieties with torsion-free nilpotent fundamental groups of high nilpotency class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23505",
  "author_total": 1,
  "authors": [
    {
      "name": "Taito Shimoji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/emk0t6s6w2txs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23505",
  "fulltext_url": null,
  "id": "emk0t6s6w2txs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23505",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
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      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
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  ],
  "openalex": "W7222959509",
  "pdf_url": "https://arxiv.org/pdf/2610.23505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/emk0t6s6w2txs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23505"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "mixed Hodge structures on the strictly upper triangular Lie algebras",
  "title_text": "mixed Hodge structures on the strictly upper triangular Lie algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/emk0t6s6w2txs",
  "venue": "arXiv",
  "versions": []
}