{
  "abstract": "Let $f:X\\to S$ be a smooth projective family, and fix a semisimple flat bundle on a fiber $X_0$. Its isomonodromic deformation determines a holomorphic section $σ_{\\mathrm{dR}}:S\\to M_{\\mathrm{dR}}(X/S)$ of the relative de Rham moduli space. Applying the relative non-abelian Hodge correspondence fiberwise gives a section $σ_{\\mathrm{Dol}}:S\\to M_{\\mathrm{Dol}}(X/S)$, whose value at each $s\\in S$ is the Higgs bundle corresponding to the flat bundle $σ_{\\mathrm{dR}}(s)$. Unlike $σ_{\\mathrm{dR}}$, the section $σ_{\\mathrm{Dol}}$ is in general only real analytic. We study the geometric consequences of its holomorphicity along a complex analytic subvariety. First, we prove an absolute lifting theorem: the relative isomonodromic Higgs bundle admits an absolute Higgs lift, and the fiberwise harmonic metrics can be modified to solve the Hitchin--Simpson equation on the total space. Second, we prove that the spectral one-form on every resolved irreducible component of the relative spectral scheme is Gauss--Manin flat. As an application, we prove the nilpotent rigidity conjecture of Hu--Sun--Yang--Zuo: if the initial Higgs field is nilpotent, then the Higgs field remains nilpotent along the entire holomorphic isomonodromic locus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12416",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianzhi Hu"
    },
    {
      "name": "Mai Shi"
    },
    {
      "name": "Kang Zuo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8yhkgst6j8nh4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12416",
  "fulltext_url": null,
  "id": "8yhkgst6j8nh4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12416",
  "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": "W7213209995",
  "pdf_url": "https://arxiv.org/pdf/2609.12416",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8yhkgst6j8nh4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2609.12416",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12416"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Holomorphic isomonodromic deformations of Higgs bundles: absolute lifting, spectral flatness, and nilpotent rigidity",
  "title_text": "Holomorphic isomonodromic deformations of Higgs bundles: absolute lifting, spectral flatness, and nilpotent rigidity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/8yhkgst6j8nh4",
  "venue": "arXiv",
  "versions": []
}