{
  "abstract": "Let $Y$ be a cubic 7-fold. When $Y$ is smooth, its Kuznetsov component is a Calabi-Yau category of dimension 3, and we construct an embedding of the Kuznetsov component into the derived category of Clifford modules over $\\mathbb{P}^4$. When $Y$ is a general cubic 7-fold singular along a line, we construct an explicit weakly crepant categorical resolution of its Kuznetsov component by the derived category of a smooth Calabi-Yau 3-fold, recovering a result of Favero-Kelly. In this construction, we express the resolution functor explicitly as a composition of geometric functors and mutations, and identify its kernel with a category equivalent to a pull-back of the derived category of a stacky curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28784",
  "author_total": 1,
  "authors": [
    {
      "name": "Peize Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vewfxnbxrn0c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28784",
  "fulltext_url": null,
  "id": "1vewfxnbxrn0c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28784",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7172270300",
  "pdf_url": "https://arxiv.org/pdf/2607.28784",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vewfxnbxrn0c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2607.28784",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28784"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Notes on the Kuznetsov component of cubic sevenfolds",
  "title_text": "Notes on the Kuznetsov component of cubic sevenfolds",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1vewfxnbxrn0c",
  "venue": "arXiv",
  "versions": []
}