{
  "abstract": "The compact four-dimensional manifold $\\mathbb{CP}_2\\# 3\\overline{\\mathbb{CP}_2}$ is known to admit a toric Kähler-Einstein metric $g_{\\text{KE}}$, but the metric is not known in closed form, which makes it difficult to draw conclusions about its geometry. In this article, we use a combination of analytic and computer-assisted techniques to produce an approximate Einstein metric $g$ described explicitly herein, and also prove that the true Einstein metric $g_{\\text{KE}}$ is close to $g$, where both the closeness and the topology are described explicitly. As an application, we prove bounds on the first invariant eigenvalue of the Laplace-Beltrami operator, and prove that this Kähler-Einstein metric does not have positive holomorphic sectional curvature everywhere.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32655",
  "author_total": 5,
  "authors": [
    {
      "name": "Timothy Buttsworth"
    },
    {
      "name": "William Hadden"
    },
    {
      "name": "Elli Heyes"
    },
    {
      "name": "Daniel Platt"
    },
    {
      "name": "Toby Wiseman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkcgadyjsbeq2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32655",
  "fulltext_url": null,
  "id": "fkcgadyjsbeq2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32655",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214714226",
  "pdf_url": "https://arxiv.org/pdf/2609.32655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkcgadyjsbeq2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2609.32655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32655"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Kähler-Einstein metric on the third Del Pezzo surface",
  "title_text": "The Kähler-Einstein metric on the third Del Pezzo surface",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/fkcgadyjsbeq2",
  "venue": "arXiv",
  "versions": []
}