{
  "abstract": "We show that the space of Bridgeland stability conditions Stab(Y) on a very general quintic threefold Y has infinitely many connected components. Using similar methods, we also prove that for a particular smooth projective (weak Fano) threefold X the braid group action on the set of full exceptional collections in Dscr^b(X) has infinitely many orbits, in particular, it is not transitive. This provides a counterexample to a conjecture of Bondal and Polishchuk from 1993. The conjecture was first disproved by Chang, Haiden, and Schroll, who constructed a family of partially wrapped Fukaya categories for which the transitivity fails. However, no counterexample of the form Dscr^b(X) for X a smooth projective variety was previously known. In addition, we show that Stab(X) also has infinitely many connected components. These are the first known examples of a smooth projective varieties whose spaces of Bridgeland stability conditions are disconnected.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.25391",
  "author_total": 1,
  "authors": [
    {
      "name": "Anya Nordskova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8kd9x12j71ka.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.25391",
  "fulltext_url": null,
  "id": "e8kd9x12j71ka",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.25391",
  "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": "W7171623197",
  "pdf_url": "https://arxiv.org/pdf/2607.25391",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8kd9x12j71ka.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2607.25391",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.25391"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Disconnected Stab(X) and infinitely many braid group orbits",
  "title_text": "Disconnected Stab(X) and infinitely many braid group orbits",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/e8kd9x12j71ka",
  "venue": "arXiv",
  "versions": []
}