{
  "abstract": "We study the Gieseker moduli space $\\mathcal{M}_{X_0}$ of stable rank-$2$, degree-$1$ vector bundles on an irreducible curve $X_0$ with one node. Its normalization is a two-step blow-up of the moduli space of generalized parabolic bundles on the normalization $\\tilde X_0$, and $\\mathcal{M}_{X_0}$ is recovered by gluing along a natural involution on the boundary. From this we compute $\\operatorname{Pic}(\\mathcal{M}_{X_0})$ and, via a Harder--Narasimhan stratification, the virtual Poincaré polynomial of $\\mathcal{M}_{X_0}$. Since the normalization morphism is small, the intersection cohomology of $\\mathcal{M}_{X_0}$ equals the ordinary cohomology of the smooth normalization, which gives a closed formula in terms of the arithmetic genus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08589",
  "author_total": 1,
  "authors": [
    {
      "name": "Sourav Das"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c4w113vh0j5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08589",
  "fulltext_url": null,
  "id": "5c4w113vh0j5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08589",
  "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/2610.08589",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c4w113vh0j5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08589",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08589"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Geometry of a semistable degeneration of moduli of vector bundles on curves",
  "title_text": "Geometry of a semistable degeneration of moduli of vector bundles on curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/5c4w113vh0j5g",
  "venue": "arXiv",
  "versions": []
}