{
  "abstract": "Given a compact complex surface with a nonflat Ricci-flat Kähler metric, we show that its holomorphic tangent bundle admits an RC-positive Hermitian metric. The proof relies on a characterization of RC-positivity through the anti-self-dual part of the Weyl operator, the Weitzenböck formula on the four dimensional Einstein manifold, and a conformal perturbation on the Ricci-flat metric. As a consequence, we prove that RC-positivity is not preserved after taking tensor, exterior, or symmetric power. Moreover, we show that RC-positivity is a strictly weaker notion than uniform RC-positivity, and that RC-positivity of holomorphic tangent bundle does not necessarily imply rational connectedness of the base manifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33656",
  "author_total": 2,
  "authors": [
    {
      "name": "You-Cheng Chou"
    },
    {
      "name": "Kuang-Ru Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0547dtmx8qqnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33656",
  "fulltext_url": null,
  "id": "0547dtmx8qqnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33656",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214806148",
  "pdf_url": "https://arxiv.org/pdf/2609.33656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0547dtmx8qqnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "RC-positivity of complex surfaces",
  "title_text": "RC-positivity of complex surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/0547dtmx8qqnf",
  "venue": "arXiv",
  "versions": []
}