{
  "abstract": "We study two notions of positivity for smooth currents on singular spaces. We show that they are not equivalent by establishing a necessary condition on the fourth Whitney cones. We also construct an explicit compact normal projective variety $X$ and a real smooth $(1,1)$-form $T$ on $X$ such that $T$ has local smooth ddc-potentials and is a Kähler current, but $T$ is not a positive form (hence not Hermitian).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04335",
  "author_total": 2,
  "authors": [
    {
      "name": "Duc-Thai Do"
    },
    {
      "name": "Duc-Viet Vu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e81grp14c5p5z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04335",
  "fulltext_url": null,
  "id": "e81grp14c5p5z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04335",
  "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": "W7211898424",
  "pdf_url": "https://arxiv.org/pdf/2609.04335",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e81grp14c5p5z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04335",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04335"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Positivity of Smooth Currents on Singular Spaces",
  "title_text": "Positivity of Smooth Currents on Singular Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/e81grp14c5p5z",
  "venue": "arXiv",
  "versions": []
}