{
  "abstract": "We study the Gieseker--Maruyama moduli space $M_{c_3}$ of stable rank 2 torsion-free sheaves on $\\mathbb{P}^3$ with Chern classes $c_1=-1$, $c_2=1$, and odd $c_3 \\le 1$. Every such sheaf $E$ has reflexive hull $E^{\\ast\\ast}$ parametrised by $M_1$, and the quotient $E^{\\ast\\ast}/E$ is a 0-dimensional sheaf of length $n = (1-c_3)/2$. We prove that $M_{c_3}$ is isomorphic to the relative Quot scheme $\\mathsf{Quot}_{\\mathbb{P}^3 \\times M_1/M_1}(\\mathscr{R},n)$, where $\\mathscr{R}$ is the universal reflexive sheaf over $M_1$. Our technique combines (i) Bridgeland-type wall-crossing in Donaldson--Thomas theory, (ii) the theory of good moduli spaces, (iii) deformation theory in dgla and Ext-quiver language. We deduce that $M_{c_3}$ is connected, and we analyse its \\emph{smoothable component} $M_{c_3}^{\\mathsf{main}}$, proving it is rational and generically smooth of dimension $4n+3$. We further prove that $\\dim \\mathrm{Sing} M_{c_3} \\geq 4n-2$ for all $n \\geq 2$. Finally, we provide a geometric characterisation for the cases $n\\leq 2$. We show that $M_{-1}$ is a smooth rational projective variety of dimension 7 and compute its motive in the Grothendieck ring of varieties, while $M_{-3}$ is shown to be an integral, normal variety of dimension 11 that is regular in codimension 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01961",
  "author_total": 4,
  "authors": [
    {
      "name": "Charles Almeida"
    },
    {
      "name": "Nicolò Bignami"
    },
    {
      "name": "Marcos Jardim"
    },
    {
      "name": "Andrea T. Ricolfi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30mc9x8d4k13y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01961",
  "fulltext_url": null,
  "id": "30mc9x8d4k13y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01961",
  "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/2611.01961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30mc9x8d4k13y.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Moduli spaces of rank 2 sheaves on $\\mathbb P^3$ via Quot schemes",
  "title_text": "Moduli spaces of rank 2 sheaves on ℙ^3 via Quot schemes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/30mc9x8d4k13y",
  "venue": "arXiv",
  "versions": []
}