{
  "abstract": "We construct a two-parameter family of complex structures on the standard six-sphere, starting from a rational elliptic surface with singular fibers $III^*,I_1,I_1,I_1$. The resulting torus fibration over $\\mathbb{P}^1$ has one multiple fiber of multiplicity four, one hexagonal fiber, and two rank-one degenerations. These complex structures are not biholomorphic to the original Alpöge--Claude examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33785",
  "author_total": 1,
  "authors": [
    {
      "name": "Jeff Viaclovsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bab1r8ywhjxsj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33785",
  "fulltext_url": null,
  "id": "bab1r8ywhjxsj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33785",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214775278",
  "pdf_url": "https://arxiv.org/pdf/2609.33785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bab1r8ywhjxsj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A two-parameter family of complex structures on $S^6$",
  "title_text": "A two-parameter family of complex structures on S^6",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/bab1r8ywhjxsj",
  "venue": "arXiv",
  "versions": []
}