{
  "abstract": "Let $M=X_6^σ$ be a smooth Debarre-Voisin hyperkähler fourfold and $X=X_3^σ$ the associated smooth hyperplane section of $\\operatorname{Gr}(3,10)$. Using the incidence correspondence between $X$ and $M$, we construct a family $\\mathcal E$ of objects in the Kuznetsov component $\\operatorname{Ku}(X)$. We write $v$ for the common Mukai vector of its fibers. We prove that the associated Mukai homomorphism \\[ Θ_{\\mathcal E}|_{v^\\perp}\\colon v^\\perp\\xrightarrow{\\sim}H^2(M,\\mathbb Z) \\] is an integral Hodge isometry and explicitly determine the inverse image of the Plücker polarization. For a very general point of the trivector divisor corresponding to discriminant $24$, we also construct an integral Hodge isometry between the full Mukai lattices of $\\operatorname{Ku}(X)$ and the associated twisted K3 surface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04602",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryo Akazawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pd6szpadzkp7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04602",
  "fulltext_url": null,
  "id": "4pd6szpadzkp7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04602",
  "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/2611.04602",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pd6szpadzkp7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04602",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04602"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "K3 Categories and Mukai Homomorphisms for Debarre-Voisin Varieties",
  "title_text": "K3 Categories and Mukai Homomorphisms for Debarre-Voisin Varieties",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/4pd6szpadzkp7",
  "venue": "arXiv",
  "versions": []
}