{
  "abstract": "Let $X$ be a compact Kähler manifold and $(α,β)$ be a pair of Kähler classes. We show that when $(α,β)$ is $J$-semistable, the collection of positive-dimensional irreducible $J$-null subvarieties is finite. We also obtain a uniform positive lower bound for the normalized $J$-slope of every irreducible non-$J$-null subvariety. This confirms the finiteness and uniform-gap expectation of Khalid-Sjöström Dyrefelt \\cite[Section 1.2, Theorem 1.5; Remark 1.8]{KSD26}. As a corollary, we show that the collection of optimal destabilizers is finite when the stability threshold is nonpositive.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14713",
  "author_total": 1,
  "authors": [
    {
      "name": "Junbang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5eykvt2fmx7sv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14713",
  "fulltext_url": null,
  "id": "5eykvt2fmx7sv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14713",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7213350134",
  "pdf_url": "https://arxiv.org/pdf/2609.14713",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5eykvt2fmx7sv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.14713",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14713"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Finiteness of null subvarieties and optimal destabilizers for the J-equation",
  "title_text": "Finiteness of null subvarieties and optimal destabilizers for the J-equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/5eykvt2fmx7sv",
  "venue": "arXiv",
  "versions": []
}