{
  "abstract": "We study the large volume limit of Bridgeland stability conditions on smooth projective varieties. For each fixed ray in a suitable angular sector, we prove that an object of $\\mathrm{D}^b(X)$ is Bridgeland (semi)stable in the corresponding hearts for all sufficiently large radii if and only if it is a pure $H$-Gieseker (semi)stable sheaf. In this sector, we identify the category of coherent sheaves as the limiting heart in the sense of eventual membership. We also identify a perverse coherent limiting heart in the opposite angular sector. The key ingredients are uniform HN-phase estimates for bounded families of pure sheaves, coefficient bounds for the coherent images of potential destabilizers, and a criterion forcing narrow exact sequences in the varying hearts to be bounded saturated coherent sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37032",
  "author_total": 1,
  "authors": [
    {
      "name": "Chunkai Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bhwhz7ym1gd1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37032",
  "fulltext_url": null,
  "id": "1bhwhz7ym1gd1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37032",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7224101657",
  "pdf_url": "https://arxiv.org/pdf/2610.37032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bhwhz7ym1gd1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bridgeland stability and Gieseker stability I: Limit stability",
  "title_text": "Bridgeland stability and Gieseker stability I: Limit stability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1bhwhz7ym1gd1",
  "venue": "arXiv",
  "versions": []
}