{
  "abstract": "We study Hodge--Tjurina numbers and the Tjurina subspectrum of isolated hypersurface singularities. We relate these invariants to Hodge ideals and microlocal $V$-filtrations and investigate their behavior under Thom--Sebastiani sums. For separated sums, we obtain a filtered defect formula and, in particular, give an affirmative answer to the question raised by Almirón concerning the Thom--Sebastiani property of the Tjurina subspectrum: it holds if and only if the Tjurina number is multiplicative. We also discuss rational sampling, spectral reconstruction, symmetry bounds, and examples illustrating the information captured and lost by integer Hodge--Tjurina data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08290",
  "author_total": 2,
  "authors": [
    {
      "name": "Shijie Zheng"
    },
    {
      "name": "Huaiqing Zuo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmz9afkhv8zwm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08290",
  "fulltext_url": null,
  "id": "fmz9afkhv8zwm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08290",
  "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": "W7220984557",
  "pdf_url": "https://arxiv.org/pdf/2610.08290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmz9afkhv8zwm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08290"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hodge--Tjurina Numbers, Tjurina Spectra, and Thom--Sebastiani Formulas",
  "title_text": "Hodge--Tjurina Numbers, Tjurina Spectra, and Thom--Sebastiani Formulas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/fmz9afkhv8zwm",
  "venue": "arXiv",
  "versions": []
}