{
  "abstract": "Let $C(v)$ denote a Schubert cell in the flag variety $\\operatorname{GL}_n/B$, and let $X(w)$ be a Schubert variety containing $C(v)$. Mellit has conjectured that, if $X(w)$ is smooth, the existence of an open $B$-orbit in the conormal bundle to $C(v)$ in $X(w)$ is equivalent to $C(w_0w)$ being contained in the smooth locus of $X(w_0v)$. We prove a stronger version of this conjecture, requiring only that $X(w)$ is factorial. We prove our result by constructing a sequence of graphs associated to the pair $v,w$ such that the existence of a cycle in one of these graphs is equivalent to the non-existence of such an open orbit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35923",
  "author_total": 1,
  "authors": [
    {
      "name": "Derek R. Aoki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82hr43p0910pd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35923",
  "fulltext_url": null,
  "id": "82hr43p0910pd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35923",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7224106636",
  "pdf_url": "https://arxiv.org/pdf/2610.35923",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82hr43p0910pd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35923",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35923"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Open Borel Orbits in Conormal Bundles to Schubert Cells",
  "title_text": "On Open Borel Orbits in Conormal Bundles to Schubert Cells",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/82hr43p0910pd",
  "venue": "arXiv",
  "versions": []
}