{
  "abstract": "We explore connections between existence of k $\\Bbbk $ double struck k -rational points for Fano varieties defined over k $\\Bbbk $ double struck k , a subfield of C $\\mathbb {C}$ double struck upper C , and existence of Kähler-Einstein metrics on their geometric models. First, we show that geometric models of del Pezzo surfaces with at worst quotient singularities defined over k ⊂ C $\\Bbbk \\subset \\mathbb {C}$ double struck k subset of double struck upper C admit (orbifold) Kähler–Einstein metrics if they do not have k $\\Bbbk $ double struck k -rational points. Then we prove the same result for smooth Fano 3-folds with 8 exceptions. Consequently, we explicitly describe several families of pointless Fano 3-folds whose geometric models admit Kähler-Einstein metrics. In particular, we obtain new examples of prime Fano 3-folds of genus 12 $12$ 12 that admit Kähler–Einstein metrics. Our result can also be used to prove existence of rational points for certain Fano varieties, for example for any smooth Fano 3-fold over k ⊂ C $\\Bbbk \\subset \\mathbb {C}$ double struck k subset of double struck upper C whose geometric model is strictly K-semistable.",
  "abstract_shown": true,
  "affiliations": [
    "University of Nottingham",
    "University of Edinburgh",
    "Saitama University",
    "Aix Marseille University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Hamid Abban",
      "orcid": "0000-0002-4260-3243"
    },
    {
      "affs": [
        1
      ],
      "name": "Ivan Cheltsov",
      "orcid": "0000-0002-6820-8073"
    },
    {
      "affs": [
        2
      ],
      "name": "Takashi Kishimoto",
      "orcid": "0000-0002-2887-0089"
    },
    {
      "affs": [
        3
      ],
      "name": "Frederic Mangolte",
      "orcid": "0000-0002-5651-2801"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0p4b75k292e3d.bib",
  "cited_by": 0,
  "doi": "10.1017/fms.2026.10266",
  "fulltext_url": null,
  "id": "0p4b75k292e3d",
  "issns": [
    "2050-5094"
  ],
  "landing_url": "https://www.cambridge.org/core/product/identifier/S2050509426102667/type/journal_article",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W4404345919",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/0p4b75k292e3d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "10.1017/fms.2026.10266",
      "source": "crossref",
      "url": "https://www.cambridge.org/core/product/identifier/S2050509426102667/type/journal_article"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Geometry and complex manifolds",
      "subfield": "geometry-topology"
    }
  ],
  "title": "K-stability of pointless del Pezzo surfaces and Fano 3-folds",
  "title_text": "K-stability of pointless del Pezzo surfaces and Fano 3-folds",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/0p4b75k292e3d",
  "venue": "Forum of Mathematics, Sigma",
  "versions": []
}