{
  "abstract": "We prove that a locally maximal plurisubharmonic function on a domain in $\\bC^n$, $n\\geq2$, is maximal if it has locally analytic singularities with a two-sided locally bounded remainder. Using McAdam's theorem, we show that local maximality forces the analytic spread of each defining ideal to be less than $n$. We use normalized blow-ups and Siu's analyticity theorem to compare singularities through generic divisorial Lelong numbers. We also obtain a criterion for maximality in terms of maximality outside the pole set and the analytic spread of the local defining ideals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05937",
  "author_total": 2,
  "authors": [
    {
      "name": "Thai Duong Do"
    },
    {
      "name": "Pham Hoang Hiep"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ce4txtjw5axr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05937",
  "fulltext_url": null,
  "id": "7ce4txtjw5axr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05937",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7220657257",
  "pdf_url": "https://arxiv.org/pdf/2610.05937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ce4txtjw5axr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.05937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Local-to-global maximality for plurisubharmonic functions with locally analytic singularities",
  "title_text": "Local-to-global maximality for plurisubharmonic functions with locally analytic singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7ce4txtjw5axr",
  "venue": "arXiv",
  "versions": []
}