{
  "abstract": "The stringy $E$-function is a fundamental invariant of varieties with log-terminal singularities, which was introduced by Batyrev as a singular analogue of the Hodge--Deligne polynomial. Its coefficients (up to an appropriate sign) are the stringy Hodge numbers $h_{\\mathrm{str}}^{p,q}(Y)$. We completely determine when these coefficients are universally non-negative:~for each triple $(n,p,q)$, we classify when $h_{\\mathrm{str}}^{p,q}(Y)\\geq 0$ for every projective Gorenstein canonical $n$-fold $Y$; we answer this question both when we assume $E_{\\mathrm{str}}(Y;u,v)$ is a polynomial and when we drop this condition. As a consequence, we settle Batyrev's non-negativity conjecture in all dimensions:~it holds in dimensions at most $4$ and fails in every dimension at least $5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07836",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiahui Huang"
    },
    {
      "name": "Matthew Satriano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5da1jn5fned8v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07836",
  "fulltext_url": null,
  "id": "5da1jn5fned8v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07836",
  "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": "W7202190152",
  "pdf_url": "https://arxiv.org/pdf/2608.07836",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5da1jn5fned8v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2608.07836",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07836"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A complete classification of negative stringy Hodge numbers",
  "title_text": "A complete classification of negative stringy Hodge numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/5da1jn5fned8v",
  "venue": "arXiv",
  "versions": []
}