{
  "abstract": "For a primitive symplectic variety $X$ admitting a holomorphic Lagrangian fibration $f: X \\to B$, we classify the possible Mumford--Tate groups of the very general fiber. We extract as a consequence that the discriminant of $f$ has codimension one in $B$. In the special case when $X$ is a hyper-Kähler manifold which is general among those admitting a Lagrangian fibration, and $b_2(X) \\geq 7$, we further show that the very general fiber of $f$ is Hodge-generic. Finally, as an application of our classification, we confirm an expectation of Li--Tosatti that when $f$ is not isotrivial, the special Kähler metric on $B$ has positive holomorphic sectional curvature on the regular values of $f$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02481",
  "author_total": 1,
  "authors": [
    {
      "name": "Edward Varvak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejgyj8mbhra6k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02481",
  "fulltext_url": null,
  "id": "ejgyj8mbhra6k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02481",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220457431",
  "pdf_url": "https://arxiv.org/pdf/2610.02481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejgyj8mbhra6k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Mumford--Tate group of a very general Lagrangian fiber",
  "title_text": "The Mumford--Tate group of a very general Lagrangian fiber",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/ejgyj8mbhra6k",
  "venue": "arXiv",
  "versions": []
}