{
  "abstract": "We classify compact Kähler--Einstein surfaces whose metric is induced by a holomorphic isometric immersion into a finite-dimensional complex projective space. No symmetry assumption and no bound on the codimension are imposed. We prove that the only such surfaces are \\[ (\\PP^2,m g_{\\FS}) \\quad\\text{and}\\quad \\bigl(\\PP^1\\times\\PP^1,m(g_{\\FS}\\oplus g_{\\FS})\\bigr), \\qquad m\\in\\mathbb Z_{>0}, \\] realized respectively by the Veronese and Segre--Veronese embeddings. The main new ingredient is a codimension-independent exclusion of the entire Fano-index-one branch, combining a common anticanonical root construction with Gram--Gauss rank estimates and, in degree five, an equivariant curvature argument. Consequently, every connected compact Kähler--Einstein surface whose metric is induced by a holomorphic isometric immersion into a finite-dimensional complex projective space is homogeneous.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22832",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrea Loi"
    },
    {
      "name": "Mirel Caibăr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1hwbkg4amwfka.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22832",
  "fulltext_url": null,
  "id": "1hwbkg4amwfka",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22832",
  "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"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214040003",
  "pdf_url": "https://arxiv.org/pdf/2609.22832",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1hwbkg4amwfka.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22832",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22832"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Projectively induced Kähler--Einstein surfaces",
  "title_text": "Projectively induced Kähler--Einstein surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/1hwbkg4amwfka",
  "venue": "arXiv",
  "versions": []
}