{
  "abstract": "We study the global topology of \\emph{fundamentally tame} Landau--Ginzburg (LG) models on complete Kähler manifolds. We first show that the superpotential $f$ is surjective onto $\\mathbb{C}$, then prove that $f$ restricts to a locally trivial fibration over the set of its regular values, which yields a global generalization of the classical Milnor fibration and provides an Ehresmann-type fibration in the non-proper setting. Assuming that $f$ has finitely many critical points, we use a Morse-theoretic argument to show that the relative homology of $\\bigl(M,f^{-1}(c)\\bigr)$, for a regular value $c$, is concentrated in the middle degree and has rank equal to the global Milnor number $μ_f$. We further identify the relative homotopy type of the fibers with that of the sublevel sets of $f$ at infinity.Finally, for deformations satisfying a uniform tameness condition on a Stein manifold, we construct the relative cohomology bundles at positive and negative infinity, each equipped with a natural flat Gauss--Manin connection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25825",
  "author_total": 2,
  "authors": [
    {
      "name": "Huijun Fan"
    },
    {
      "name": "Jieran Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ew8q23mzdcymv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25825",
  "fulltext_url": null,
  "id": "ew8q23mzdcymv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25825",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223000857",
  "pdf_url": "https://arxiv.org/pdf/2610.25825",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ew8q23mzdcymv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25825",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25825"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Cohomological Milnor Fibrations of Landau--Ginzburg Models",
  "title_text": "Cohomological Milnor Fibrations of Landau--Ginzburg Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/ew8q23mzdcymv",
  "venue": "arXiv",
  "versions": []
}