{
  "abstract": "Let $X$ be a compact connected Riemann surface and $S\\,\\subset\\, X$ a finite subset. We consider parabolic principal $G$--bundles $\\mathcal{E}_{G}$ on $X$ with parabolic structure on $S$, where $G$ is a connected complex reductive affine algebraic group. Let $P\\, \\subset\\, G$ be a parabolic subgroup and $\\mathcal{E}_{P}\\, \\subset\\, \\mathcal{E}_{G}$ a reduction of structure group of $\\mathcal{E}_{G}$ to $P$. We give a criterion for the existence of a parabolic Lie algebroid connection on $\\mathcal{E}_{P}$ for any given parabolic Lie algebroid on $(X,\\,S)$ whose anchor map is not surjective. More precisely, $\\mathcal{E}_{P}$ admits a parabolic Lie algebroid connection if the reduction $\\mathcal{E}_{P}\\, \\subset\\, \\mathcal{E}_{G}$ is parabolically infinitesimally rigid. In particular, the Harder--Narasimhan reduction of $\\mathcal{E}_{G}$ admits a parabolic Lie algebroid connection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01402",
  "author_total": 2,
  "authors": [
    {
      "name": "Indranil Biswas"
    },
    {
      "name": "Pritthijit Biswas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ts5dhsmtgxh7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01402",
  "fulltext_url": null,
  "id": "3ts5dhsmtgxh7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01402",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.01402",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ts5dhsmtgxh7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01402",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01402"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Parabolic Lie algebroid connections on parabolic principal bundles over curves",
  "title_text": "Parabolic Lie algebroid connections on parabolic principal bundles over curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/3ts5dhsmtgxh7",
  "venue": "arXiv",
  "versions": []
}