{
  "abstract": "Let $X$ be a normal affine variety over an algebraically closed field of characteristic zero. Through the lens of non-Archimedean geometry, we study the space of polarized compactifications of $X$, consisting of pairs $(\\bar X, D)$ where $\\bar X$ is a normal projective variety containing $X$ as a dense open subset, and $D$ is an effective ample $\\mathbb{Q}$-Cartier $\\mathbb{Q}$-divisor with support equal to the complement of $X$ in $\\bar X$. We identify this space with a natural class of functions--the Fubini--Study functions--on the Berkovich analytification of $X$. Through a Rees correspondence, we also give a bijection with the space of homogeneous $\\mathbb{Q}$-valued, finitely generated negative non-Archimedean norms (or filtrations) on the coordinate ring of $X$. Using the above identifications, we equip the space of polarized compactifications, and numerical classes thereof, with natural metrics and identify the metric completions. The latter include a space of continuous plurisubharmonic functions in the sense of Chambert-Loir and Ducros, and a space of birational curve classes as studied by Dang and Favre.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21838",
  "author_total": 2,
  "authors": [
    {
      "name": "Mattias Jonsson"
    },
    {
      "name": "Yueqiao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq8sxzhm6brnh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21838",
  "fulltext_url": null,
  "id": "eq8sxzhm6brnh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21838",
  "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": "W7222694439",
  "pdf_url": "https://arxiv.org/pdf/2610.21838",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq8sxzhm6brnh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21838",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21838"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The space of polarized compactifications of an affine variety",
  "title_text": "The space of polarized compactifications of an affine variety",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/eq8sxzhm6brnh",
  "venue": "arXiv",
  "versions": []
}