{
  "abstract": "The aim of this paper is to study the Segre invariant for rank $2$ vector bundles on Hirzebruch surfaces $\\mathbb{F}_e$, $e \\geq 0$. We give necessary conditions in order to determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle on $\\mathbb{F}_e$ with fixed Chern classes. We compute a bound of the dimensions of the strata whenever are non-empty. Finally, we present applications to Brill-Noether Theory and describe differences between moduli spaces under change of polarization for rank $2$ vector bundles on $\\mathbb{F}_e$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30236",
  "author_total": 1,
  "authors": [
    {
      "name": "L. Roa-Leguizamón"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eghq12q3qcf5t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30236",
  "fulltext_url": null,
  "id": "eghq12q3qcf5t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30236",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204870299",
  "pdf_url": "https://arxiv.org/pdf/2608.30236",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eghq12q3qcf5t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30236",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30236"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces",
  "title_text": "A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/eghq12q3qcf5t",
  "venue": "arXiv",
  "versions": []
}