{
  "abstract": "Lagrangians of the moduli space of Higgs bundles are a fundamental piece of its study under the lens of mirror symmetry. We construct a new class of Lagrangians defined via a zero 'velocity condition' imposed on the natural action of the non-zero complex numbers on the moduli space, motivated by a certain 'infinitesimal conormal principle'. These are Lagrangian subvarieties analogous to the upward flows considered by [CW19] and [HH22], but which fiber over the $\\mathbb{C}^*$-fixed point subvarieties. We then prove a formula for the number of intersection points of this Lagrangian with the generic fiber of the Hitchin map, and build a vector bundle over the dual moduli space which we conjecture to correspond to its mirror hyperholomorphic bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38548",
  "author_total": 3,
  "authors": [
    {
      "name": "Peter Gothen"
    },
    {
      "name": "André Oliveira"
    },
    {
      "name": "Rodrigo Pereira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/41aas6nex9k0n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38548",
  "fulltext_url": null,
  "id": "41aas6nex9k0n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38548",
  "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": "W7215082343",
  "pdf_url": "https://arxiv.org/pdf/2609.38548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/41aas6nex9k0n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Zero velocity Lagrangians in the Hitchin system",
  "title_text": "Zero velocity Lagrangians in the Hitchin system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/41aas6nex9k0n",
  "venue": "arXiv",
  "versions": []
}