{
  "abstract": "We study the marked analytic moduli space of polystable degree-zero $\\mathrm{SL}_r(\\C)$-Higgs bundles over Teichmüller space. The connected components of the orbit-type loci defined by the full determinant-one stabilizers form a complex Whitney stratification. The projection to Teichmüller space is a holomorphic submersion on every stratum. Each stratum carries a canonical relative holomorphic symplectic form. These forms determine a vertical holomorphic Poisson bracket on the reduced structure sheaf, whose symplectic leaves are the connected orbit-type strata in the fibers. On each fiber, the Hitchin--Kobayashi correspondence is biholomorphic on every stratum and identifies its hyperkähler structure. The harmonic representatives and vertical hyperkähler tensors vary smoothly along the strata of the total space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00378",
  "author_total": 1,
  "authors": [
    {
      "name": "Shiyu Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kwg8qjk1qttk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00378",
  "fulltext_url": null,
  "id": "8kwg8qjk1qttk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00378",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7215752123",
  "pdf_url": "https://arxiv.org/pdf/2610.00378",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kwg8qjk1qttk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00378",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00378"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stratification of Joint Moduli Spaces of Higgs Bundles",
  "title_text": "Stratification of Joint Moduli Spaces of Higgs Bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/8kwg8qjk1qttk",
  "venue": "arXiv",
  "versions": []
}