{
  "abstract": "This paper is to construct deformation families of open Calabi-Yau manifolds together with some discussions on Steinness. Firstly, we construct a nontrivial compactifiable deformation of open Calabi-Yau manifolds from rational elliptic surface with global sections. Secondly, we give a condition for the existence of an elliptic fibration with global sections on the complex analytic family of rational elliptic surface with global sections, construct a holomorphic involution on the compactifiable deformation family and claim the non-Steinness for all the compactifiable deformation families constructed. Finally, we give some discussions on the non-Steinness of the quasi-projective variety from $\\text{CP}^2 \\text{$\\#$9} \\overline{\\text{CP}}^2$ corresponding to a conjecture by Marco Brunella and construct deformation families whose fibers were conjectured to be Stein by Andreas Höring and Thomas Peternel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10454",
  "author_total": 1,
  "authors": [
    {
      "name": "Fan Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8vr8qrs83768.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10454",
  "fulltext_url": null,
  "id": "f8vr8qrs83768",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10454",
  "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": "W7212188849",
  "pdf_url": "https://arxiv.org/pdf/2609.10454",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8vr8qrs83768.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.10454",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10454"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Deformation families of open Calabi-Yau manifolds and Steinness",
  "title_text": "Deformation families of open Calabi-Yau manifolds and Steinness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/f8vr8qrs83768",
  "venue": "arXiv",
  "versions": []
}