{
  "abstract": "We study the action of the Serre functor of smooth proper dg categories at their Hochschild-Serre algebra, and the invariant sub-aglebra of the Serre functor. As applications, we prove some theorems of categorical Torelli. Namely, let $\\Ku(\\X)$ be the Kuznetsov component of degree $d$ smooth hypersurface in weighted projective space $\\mathbb{P}(a_0, a_1, \\cdots, a_n)$, where the common maximal divisor $\\gcd(d, \\sum^{n}_{i=0}a_{i})=1$. We show the categorical Torelli for $\\Ku(\\X)$. We show that the $\\mathbb{C}^{\\ast}$ equivariant matrix factorization category associated with a quasi-homogeneous polynomial function $f$ that has an isolated singularity together with a twisted functor $\\{1\\}$ reconstructs $f$ up to an isomorphism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07562",
  "author_total": 1,
  "authors": [
    {
      "name": "Xun Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/546jyeq7y7nma.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07562",
  "fulltext_url": null,
  "id": "546jyeq7y7nma",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07562",
  "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": "W7212010638",
  "pdf_url": "https://arxiv.org/pdf/2609.07562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/546jyeq7y7nma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Group action of Hochschild-Serre algebra and categorical reconstruction",
  "title_text": "Group action of Hochschild-Serre algebra and categorical reconstruction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/546jyeq7y7nma",
  "venue": "arXiv",
  "versions": []
}