{
  "abstract": "In this paper, we investigate the moduli space of algebraic asymptotic hyperkähler structures on hyperkähler quotients arising from a quaternionic vector space $\\mathbb{H}^n$. We consider the period map on this moduli space, and prove a Torelli-type theorem (i.e., the bijectivity of the period map) under mild assumptions including the surjectivity of the Kirwan map. This work provides an algebro-geometric generalization of the Torelli-type theorem for ALE gravitational instantons by Kronheimer (1989). In particular, this theorem applies to toric hyperkähler varieties and Nakajima quiver varieties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08680",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryota Kotani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nx57xk5bcpf6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08680",
  "fulltext_url": null,
  "id": "6nx57xk5bcpf6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08680",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7202195960",
  "pdf_url": "https://arxiv.org/pdf/2608.08680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nx57xk5bcpf6.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:28Z",
      "native_id": "2608.08680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Torelli-type theorem for hyperkähler quotients",
  "title_text": "A Torelli-type theorem for hyperkähler quotients",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/6nx57xk5bcpf6",
  "venue": "arXiv",
  "versions": []
}