{
  "abstract": "Suppose $n\\ge2$ and $K\\subset\\C^n$ is compact and polynomially convex. Write $q(z)=(e^{-iz_1},\\ldots,e^{-iz_n})$, $X_K=(\\C^*)^n\\setminus(K\\cap(\\C^*)^n)$, and $Y_K=\\C^n\\setminus q^{-1}(K)$. We prove that $X_K$ and its logarithmic covering $Y_K$ are Oka. More strongly, $Y_K$ admits normalized holomorphic families of entire embeddings through prescribed holomorphic sections. The proof combines polynomial pair Hamiltonian transport in multiplicative coordinates, compatible with the coordinate hyperplanes, with a fixed Fatou--Bieberbach model. Applications include Oka slab crosses over arbitrary nonempty connected planar domains, complements of periodic equal-radius Euclidean balls centered at products of planar lattices, and complements of sufficiently small closed metric balls in products of elliptic curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15433",
  "author_total": 4,
  "authors": [
    {
      "name": "Yun-Heng Du"
    },
    {
      "name": "Bin Guo"
    },
    {
      "name": "Peng-Chao Wang"
    },
    {
      "name": "Song-Yan Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rnhj32a8hzd7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15433",
  "fulltext_url": null,
  "id": "8rnhj32a8hzd7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15433",
  "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": "W7221824797",
  "pdf_url": "https://arxiv.org/pdf/2610.15433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rnhj32a8hzd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.15433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15433"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Oka complements in algebraic tori and their logarithmic covers",
  "title_text": "Oka complements in algebraic tori and their logarithmic covers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8rnhj32a8hzd7",
  "venue": "arXiv",
  "versions": []
}