{
  "abstract": "We study Stein neighborhood bases for unions of closed complex and totally real submanifolds, with particular attention to a linear configuration with noncompact intersection. We prove that the set $X=\\{w=0\\}\\cup\\{\\Im z=\\Im w=0\\}\\subset\\C^2$ admits a Stein neighborhood basis. The proof starts from the explicit plurisubharmonic defining function $ρ(z,w)=(\\Im w)^2+\\sinh^2(\\Im z)|w|^2$ and obtains the necessary non-uniform control at infinity by adding a locally uniformly convergent series of nonnegative plurisubharmonic terms constructed by Oka--Weil approximation. We also give an example of a closed complex submanifold and a closed totally real submanifold in $\\C^2$ with compact intersection whose union has no Stein neighborhood basis, showing that the unrestricted union problem has a negative answer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10191",
  "author_total": 1,
  "authors": [
    {
      "name": "Ovidiu Preda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j5vb275dtfg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10191",
  "fulltext_url": null,
  "id": "1j5vb275dtfg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10191",
  "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": "W7212129279",
  "pdf_url": "https://arxiv.org/pdf/2609.10191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j5vb275dtfg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10191",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10191"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stein neighborhood bases for complex--totally real unions",
  "title_text": "Stein neighborhood bases for complex--totally real unions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/1j5vb275dtfg1",
  "venue": "arXiv",
  "versions": []
}