{
  "abstract": "Let $U$ be a smooth affine variety of the form $U=\\mathrm{P}^n\\setminus H$, where $H\\subset\\mathrm{P}^n$ is a smooth connected hypersurface. We prove that every smooth projective compactification of the complex manifold $U$, by adding a smooth connected divisor, is isomorphic to $\\mathrm{P}^n$. The proof uses the rational Reeb index of the normal circle bundle and positive $S^1$-equivariant symplectic homology. This paper is motivated by the work of Chi Li and Zhengyi Zhou, and makes a generalization to their result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38376",
  "author_total": 1,
  "authors": [
    {
      "name": "Hairun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dtznfjey70p8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38376",
  "fulltext_url": null,
  "id": "dtznfjey70p8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38376",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38376",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dtznfjey70p8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38376",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38376"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Projective compactifications of hypersurface complements",
  "title_text": "Projective compactifications of hypersurface complements",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dtznfjey70p8z",
  "venue": "arXiv",
  "versions": []
}