{
  "abstract": "We study Jack Lee's conjecture that, for a compact strictly pseudoconvex CR manifold $M$, the condition $c_1(T^{1,0}M)=0$ in $H^2(M,\\mathbb{R})$ implies the existence of a pseudo-Einstein structure. For links of isolated singularities, we construct counterexamples in every odd dimension at least three, with $c_1(T^{1,0}M)=0$ in $H^2(M,\\mathbb{Z})$ and $b_1(M)=0$. For isolated algebraic singularities of log canonical type and complex dimension at least three, we prove that the real Chern class condition is equivalent to $\\mathbb{Q}$-Cartierness of the canonical divisor, log canonicity, and the existence of a pseudo-Einstein structure. Finally, we construct a Du Bois threefold singularity whose link satisfies the real Chern class condition but admits no pseudo-Einstein structure. The initial versions of the proofs were generated with AI assistance and were subsequently revised and verified by the authors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04851",
  "author_total": 4,
  "authors": [
    {
      "name": "Yoshinori Gongyo"
    },
    {
      "name": "Kengo Hirachi"
    },
    {
      "name": "Shuya Matsumoto"
    },
    {
      "name": "Yuya Takeuchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zk5jggwk1has.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04851",
  "fulltext_url": null,
  "id": "8zk5jggwk1has",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04851",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zk5jggwk1has.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Pseudo-Einstein Structures on Links of Isolated Singularities",
  "title_text": "Pseudo-Einstein Structures on Links of Isolated Singularities",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/8zk5jggwk1has",
  "venue": "arXiv",
  "versions": []
}