{
  "abstract": "In this paper, we investigate the geometry of the Gieseker moduli space of semistable rank $2$ torsion-free sheaves on $\\mathbb{P}^3$ with Chern classes $(c_1, c_2, c_3) = (-1, c_2, c_2^2-2)$ for $c_2 \\geq 2$. We use the modular Serre correspondence to relate these moduli spaces to spaces of pairs and to suitable Hilbert schemes of one-dimensional subschemes in $\\mathbb{P}^3$. For $c_2 \\geq 4$, we prove that the moduli space is irreducible of dimension $c_2^2+3c_2+5$. For the case $c_2 = 3$, relying on a known geometric description of a relevant Hilbert scheme, we show that the moduli space $\\mathcal{M}(-1,3,7)$ consists of exactly two irreducible components, namely the generic component of reflexive sheaves and a $T$-component, and we prove that their intersection is nonempty.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32668",
  "author_total": 3,
  "authors": [
    {
      "name": "Charles Almeida"
    },
    {
      "name": "Marcos Jardim"
    },
    {
      "name": "Leonardo Oliveira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4z35t9v7697wm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32668",
  "fulltext_url": null,
  "id": "4z35t9v7697wm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32668",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214795271",
  "pdf_url": "https://arxiv.org/pdf/2609.32668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4z35t9v7697wm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32668"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The moduli space of torsion-free sheaves with quasi-maximal third Chern class",
  "title_text": "The moduli space of torsion-free sheaves with quasi-maximal third Chern class",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4z35t9v7697wm",
  "venue": "arXiv",
  "versions": []
}