{
  "abstract": "We establish a strong Hodge decomposition theorem for Novikov type Landau--Ginzburg models, that is, triples $(M,g,θ)$ consisting of a non-compact complete Kähler manifold $(M,g)$ and a non-trivial closed holomorphic one-form $θ$ on $M$.Under the well-tameness condition and under the assumption that $M$ is Stein, we prove that the space of $L^{2}$-forms on $M$ admits an orthogonal decomposition into the space of harmonic forms of the twisted Laplacian $Δ_θ$ and the images of the twisted Dolbeault operators $\\bar\\partial+θ\\wedge$ and $\\bar\\partial^{\\dagger}+ι_{\\barθ^{\\sharp}}$; moreover, the harmonic space is concentrated in degree $n=\\dim_{\\C}M$ and is isomorphic to the Milnor rings of $θ$. As applications, we endow the complement of a hyperplane arrangement with a complete cylindrical Kähler metric, and we show that the differential of a master function with nonresonant weights is well-tamed with respect to this metric. After passing to a log resolution in the non-normal-crossing case; we then apply the results to the Yang--Yang functional of the Gaudin model, whose critical points are the Bethe roots: the top-degree harmonic space is described by the corresponding Milnor rings, and the number of Bethe roots is given by the Varchenko--Orlik--Terao lattice formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27517",
  "author_total": 2,
  "authors": [
    {
      "name": "Huijun Fan"
    },
    {
      "name": "Jieran Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7b8f0g7dbpxd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27517",
  "fulltext_url": null,
  "id": "f7b8f0g7dbpxd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27517",
  "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|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223134557",
  "pdf_url": "https://arxiv.org/pdf/2610.27517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7b8f0g7dbpxd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27517"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hodge Theory of Novikov Type Landau--Ginzburg Models",
  "title_text": "Hodge Theory of Novikov Type Landau--Ginzburg Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/f7b8f0g7dbpxd",
  "venue": "arXiv",
  "versions": []
}