{
  "abstract": "We study four of Manton's five vortex equations on a Riemann surface $X$ in relation to anti-self-dual connections. From a solution of each vortex equation, we construct an equivariant holomorphic bundle over $X$$\\times$$\\mathbb{P}^1$, $X$$\\times$$Δ$, or $X$$\\times$$\\mathbb{C}$, together with an invariant Hermitian or pseudo-Hermitian metric whose associated connection is anti-self-dual. The equivariant structures are given by the actions of $SU(2)$, $SU(1,1)$, and $SE(2)$, respectively. Conversely, we show that an equivariant holomorphic bundle equipped with an invariant (pseudo-)Hermitian metric gives rise to a solution of the corresponding vortex equation when the associated connection is anti-self-dual.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05962",
  "author_total": 1,
  "authors": [
    {
      "name": "Takashi Ono"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9dx5kqvz2jkkk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05962",
  "fulltext_url": null,
  "id": "9dx5kqvz2jkkk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05962",
  "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.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7220721192",
  "pdf_url": "https://arxiv.org/pdf/2610.05962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9dx5kqvz2jkkk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05962"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Manton's Vortex Equations and Anti-Self-Dual Connections",
  "title_text": "Manton's Vortex Equations and Anti-Self-Dual Connections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/9dx5kqvz2jkkk",
  "venue": "arXiv",
  "versions": []
}