{
  "abstract": "For a compact Riemann surface $X$, Simpson associated to each stable graded Higgs bundle $(E,θ)$ a locus $W_{[(E,θ)]}^1 \\subset M_{\\mathrm{dR}}(X,n)$, consisting of flat bundles that admit a Simpson filtration whose associated graded Higgs bundle is $(E,θ)$. He conjectured that $W_{[(E,θ)]}^1$ is Zariski closed in $M_{\\mathrm{dR}}(X,n)$. We prove this conjecture in arbitrary rank. The proof is based on the Quillen geometry of the determinant-of-cohomology line bundle over the moduli of holomorphic bundles. To any holomorphic family of flat bundles, we associate a determinant-of-cohomology line bundle equipped with a canonical holomorphic determinant connection, and derive explicit formulas for its curvature. For a family of flat bundles in $W_{[(E,θ)]}^1$, we then prove that the determinant connection form is exact. This exactness forces the associated determinant frame to extend as a nowhere-vanishing frame across any one-parameter degeneration, which controls the limiting filtration and yields the desired closedness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03542",
  "author_total": 1,
  "authors": [
    {
      "name": "Tianzhi Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1v5dk9ehj2jxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03542",
  "fulltext_url": null,
  "id": "1v5dk9ehj2jxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03542",
  "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": "W7220448980",
  "pdf_url": "https://arxiv.org/pdf/2610.03542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1v5dk9ehj2jxn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Simpson's closedness conjecture in arbitrary rank",
  "title_text": "Simpson's closedness conjecture in arbitrary rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1v5dk9ehj2jxn",
  "venue": "arXiv",
  "versions": []
}