{
  "abstract": "This is a continuation of our previous paper on toric gravitational instantons. We develop a systematic theory of compact simply-connected Einstein four-manifolds with toric symmetry. Applications include (1) The construction of simply connected positive Einstein four-manifolds with arbitrarily large $b_2$. Our method is based on local gluing combined with a global virtual counting argument. The key idea involves a particular design of rod structures to enable a gluing construction and restrict possible degenerations. (2) A topological characterization of algebraically special toric Einstein metrics. This uses special curvature identities for $W^+$ in the toric setting. (3) Uniqueness, up to scaling and isometry, on toric four-manifolds admitting algebraically special Einstein metrics. The proofs uses a variational study of the Einstein--Hilbert functional. (4) Diffeomorphism classification of compact toric Einstein four-manifolds in terms of an improved Hitchin-Thorpe inequality $χ\\geq3|τ|$. In particular, our construction recovers all the classical toric Einstein metrics, including the Page and Chen--LeBrun--Weber metrics, starting from the round sphere through moduli spaces of conical Einstein metrics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10425",
  "author_total": 2,
  "authors": [
    {
      "name": "Mingyang Li"
    },
    {
      "name": "Song Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2j6n8m37782k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10425",
  "fulltext_url": null,
  "id": "a2j6n8m37782k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10425",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
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      "arxiv",
      "math.DG"
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      "2608|Geometry and complex manifolds"
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  "openalex": "W7221019204",
  "pdf_url": "https://arxiv.org/pdf/2610.10425",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2j6n8m37782k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10425",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10425"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Compact toric Einstein four-manifolds",
  "title_text": "Compact toric Einstein four-manifolds",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:27Z",
  "url": "https://research.draconitic.com/paper/a2j6n8m37782k",
  "venue": "arXiv",
  "versions": []
}