{
  "abstract": "We study two boundary cases of the stability condition for the $J$-equation. First, under the $J$-semistable condition, we show that the destabilizing prime divisors form an exceptional family in the sense of Boucksom, with a uniform numerical gap away from them. The related modified nef estimate can remove the $J$-big assumption in Liu's work~\\cite{Liu2026Boundary}. Second, under the smooth boundary cone condition, we obtain a uniform global $C^0$ estimate for solutions of the approximating twisted $J$-equations. As a consequence, we construct a bounded-potential Bedford--Taylor solution of the $J$-equation, which is smooth outside the destabilizing prime divisors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29736",
  "author_total": 2,
  "authors": [
    {
      "name": "Jixiang Fu"
    },
    {
      "name": "Ziyi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vhadqacb83ry.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29736",
  "fulltext_url": null,
  "id": "7vhadqacb83ry",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29736",
  "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.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7204934470",
  "pdf_url": "https://arxiv.org/pdf/2608.29736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vhadqacb83ry.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Boundary Cases of the $J$-Equation: Divisorial Rigidity and a Global $C^0$ Estimate",
  "title_text": "Boundary Cases of the J-Equation: Divisorial Rigidity and a Global C^0 Estimate",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/7vhadqacb83ry",
  "venue": "arXiv",
  "versions": []
}