{
  "abstract": "Let $D\\subset\\mathbb{P}^n$, $n\\geqslant2$, be an arbitrary cubic hypersurface, and let $D_{\\mathrm{red}}$ denote its reduced support. We prove that $\\mathbb{P}^n\\setminus D$ is holomorphically elliptic, and hence Oka, unless $D_{\\mathrm{red}}$ is the union of three distinct hyperplanes containing a common codimension-two linear subspace. In the exceptional case, $\\mathbb{P}^n\\setminus D\\cong(\\mathbb{C}\\setminus\\{0,1\\})\\times\\mathbb{C}^{n-1}$, so the complement is not Oka. As applications, we prove that, for every elliptic curve $E$, the space of degree-three holomorphic maps $E\\to\\mathbb{P}^1$, and the space of degree-three holomorphic self-maps of $\\mathbb{P}^1$, are both holomorphically elliptic, and hence Oka. The second application is connected with the classification through an irreducible cubic hypersurface in $\\mathbb{P}^4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02413",
  "author_total": 1,
  "authors": [
    {
      "name": "Song-Yan Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pfg9ed34jghn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02413",
  "fulltext_url": null,
  "id": "7pfg9ed34jghn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02413",
  "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": "W7172378003",
  "pdf_url": "https://arxiv.org/pdf/2608.02413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pfg9ed34jghn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2608.02413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Elliptic complements of cubic hypersurfaces",
  "title_text": "Elliptic complements of cubic hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/7pfg9ed34jghn",
  "venue": "arXiv",
  "versions": []
}