{
  "abstract": "In this paper, we study logarithmic Donaldson-Thomas invariants for local log Calabi-Yau $4$-folds with simple normal crossing divisors. Using the family version of shifted Lagrangian classes announced by Khan-Kinjo-Park-Safronov, we construct relative and family logarithmic $\\mathsf{DT}_4$-theories for logarithmic Hilbert schemes of curves, and prove a degeneration formula. For logarithmic Hilbert schemes of points, we construct virtual classes and prove a degeneration formula in Chow groups; in particular, it is independent of shifted Lagrangian classes. Finally, combining our degeneration formula with logarithmic cobordism, we explicitly compute the zero-dimensional logarithmic $\\mathsf{DT}_4$-invariants for local surface snc pairs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17720",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaolong Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecc5w5xze62m3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17720",
  "fulltext_url": null,
  "id": "ecc5w5xze62m3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17720",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
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      "arxiv",
      "math.MP"
    ],
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7213504722",
  "pdf_url": "https://arxiv.org/pdf/2609.17720",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecc5w5xze62m3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.17720",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17720"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds",
  "title_text": "On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ecc5w5xze62m3",
  "venue": "arXiv",
  "versions": []
}