{
  "abstract": "Let $T$ be a positive $dd^c$-closed current of bidimension $(q,q)$ on a compact Kähler manifold $X$. For every $c>0$, let $E_c(T)$ be the set of points of $X$ where the Lelong number of $T$ is larger or equal to $c$. We show that $E_c(T)$ is an analytic subset of dimension at most $q$ of $X$. Moreover, the following Siu decomposition holds $$T=\\sum_{i\\in I} λ_i[V_i] +T_0,$$ where $\\{V_i\\}_{i\\in I}$ is a (possibly empty) finite or countable family of compact analytic subsets of dimension $q$ in $X$, $λ_i\\in\\mathbb{R}^+$, and $T_0$ is a positive $dd^c$-closed current such that $E_c(T_0)$ is an analytic subset of dimension at most $q-1$ of $X$ for every $c>0$. The proof relies on the duality between the pseudoeffective cone and the movable cone of a compact Kähler manifold, recently obtained by Tosatti (2026), together with a theorem of Vigny (2009) and the theory of density currents for positive $dd^c$-closed currents developed by Sibony, the first and third authors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29680",
  "author_total": 3,
  "authors": [
    {
      "name": "Tien-Cuong Dinh"
    },
    {
      "name": "Duc-Bao Nguyen"
    },
    {
      "name": "Viet-Anh Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7m3x7abxzdb7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29680",
  "fulltext_url": null,
  "id": "f7m3x7abxzdb7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29680",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7166657801",
  "pdf_url": "https://arxiv.org/pdf/2606.29680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7m3x7abxzdb7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2606.29680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Siu's analyticity theorem for positive pluriharmonic currents",
  "title_text": "Siu's analyticity theorem for positive pluriharmonic currents",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/f7m3x7abxzdb7",
  "venue": "arXiv",
  "versions": []
}