{
  "abstract": "We establish an analogue of André Weil's classical theorem for irreducible nodal curves. Let \\(X_0\\) be an irreducible projective nodal curve. We prove that an indecomposable vector bundle or torsion-free coherent sheaf \\(E\\) on \\(X_0\\) admits a holomorphic logarithmic connection \\(\\nabla\\colon E\\to E\\otimesω_{X_0}\\) with respect to the dualizing sheaf if and only if \\(°E=0\\). Moreover, when \\(°E=0\\), such a connection can be chosen so that the induced logarithmic connection on the normalization has scalar residues \\(λ\\cdot I\\) at one preimage of the node and \\(-λ\\cdot I\\) at the other, for some \\(λ\\in\\mathbb{C}\\). Explicit one-parameter families of flat connections are constructed on the irreducible rational nodal cubic curve as an illustration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29827",
  "author_total": 1,
  "authors": [
    {
      "name": "Sourav Das"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3pw9sh6k8x88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29827",
  "fulltext_url": null,
  "id": "b3pw9sh6k8x88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29827",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.29827",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3pw9sh6k8x88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29827",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29827"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weil's Theorem for Logarithmic Connections on Irreducible Nodal Curves",
  "title_text": "Weil's Theorem for Logarithmic Connections on Irreducible Nodal Curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/b3pw9sh6k8x88",
  "venue": "arXiv",
  "versions": []
}