{
  "abstract": "With any holomorphic vector bundle $E$ over a compact base one can associate a line bundle, denoted $O_{PE}(1)$. According to a conjecture of Griffiths, if $O_{PE}(1)$ admits a positively curved hermitian metric $k$, then $E$ also admits a positively curved hermitian metric, $h$. In this paper we show that, while the conjecture may be correct, it is not possible to obtain $h$ out of $k$ by a fiberwise construction that is functorial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00326",
  "author_total": 1,
  "authors": [
    {
      "name": "Laszlo Lempert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1t5rhajfpt4tv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00326",
  "fulltext_url": null,
  "id": "1t5rhajfpt4tv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00326",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7206213201",
  "pdf_url": "https://arxiv.org/pdf/2609.00326",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1t5rhajfpt4tv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00326",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00326"
    }
  ],
  "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": "On a construction of hermitian metrics on holomorphic vector bundles",
  "title_text": "On a construction of hermitian metrics on holomorphic vector bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/1t5rhajfpt4tv",
  "venue": "arXiv",
  "versions": []
}