{
  "abstract": "In this note, we show that the Hilbert scheme $\\text{Hilb}_{P_{d,4}(t)}(E_6/P_6)$ associated with the Hilbert polynomial $P_{d,4}(t)$ is disconnected by determining that it has exactly two connected components. This result adapts Seong's methods, successfully extending the disconnectedness of Grassmannians to the exceptional type $E_6$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06541",
  "author_total": 1,
  "authors": [
    {
      "name": "Minyoung Jeon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d08wk7ax80y3h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06541",
  "fulltext_url": null,
  "id": "d08wk7ax80y3h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06541",
  "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.CO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  ],
  "openalex": "W7212078856",
  "pdf_url": "https://arxiv.org/pdf/2609.06541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d08wk7ax80y3h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.06541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Disconnectedness of the Hilbert Schemes of $E_6/P_6$",
  "title_text": "Disconnectedness of the Hilbert Schemes of E_6/P_6",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/d08wk7ax80y3h",
  "venue": "arXiv",
  "versions": []
}