{
  "abstract": "We construct two families of compact complex threefolds fibred over $\\mathbb P^1$ by two-dimensional complex tori. For each positive integer $r$ and each parameter $c$ in a fixed half-plane, the families $Y_{r,c}$ and $Z_{r,c}$ have two multiple fibres of multiplicities $(4,6)$ and $(3,6)$, respectively, and one reduced normal-crossings fibre whose normalization consists of $r$ del Pezzo surfaces of degree six. Their fundamental groups are $\\mathbb Z/2$ and $\\mathbb Z/3$, respectively, and both have Euler characteristic $2r$. We compute their integral homology; the index-one members are rational homology six-spheres. Every member has algebraic dimension one, lies outside Fujiki's class $\\mathcal C$, and has connected automorphism group $\\mathbb C^*$. For fixed type and index, two members are biholomorphic exactly when their parameters differ by an element of $(6/r)\\mathbb Z$. Each underlying smooth six-manifold therefore supports uncountably many pairwise non-biholomorphic complex structures. The arithmetic input classifies finite monodromy pairs and their integral lifts to a parabolic Jacobi group acting on a rank-four lattice. A quadratic form controls integral lifting and, on the rank-two square-zero locus, computes the monodromy saturation index. We prove that the relevant invariant tensors persist under finite-index restriction, which extends the construction to arbitrary compact base curves. We also construct translation twists after base change, establish a local periodic toroidal quotient theorem in arbitrary dimension, and determine the additive Bockstein spectral sequences of the original threefolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29666",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiufan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxhmjva6pppva.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29666",
  "fulltext_url": null,
  "id": "cxhmjva6pppva",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29666",
  "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|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214362971",
  "pdf_url": "https://arxiv.org/pdf/2609.29666",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxhmjva6pppva.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29666",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29666"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Compact Complex Threefolds Fibred by Two-Dimensional Complex Tori",
  "title_text": "Compact Complex Threefolds Fibred by Two-Dimensional Complex Tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/cxhmjva6pppva",
  "venue": "arXiv",
  "versions": []
}