{
  "abstract": "We relate the spectrum of singularities to the geometry of degenerating Calabi-Yau manifolds through holomorphic analytic torsion. We express the leading asymptotic coefficients of the analytic torsion of holomorphic differential forms in terms of Hodge-theoretic invariants of vanishing cycles. For isolated hypersurface singularities, these formulas lead to the formulation of new higher Durfee-Saito conjectures bounding Hodge-filtration dimensions by the Milnor number and Eulerian numbers. We also prove that, for isolated quasi-homogeneous singularities, the spectral measure is dominated in convex order by the corresponding Irwin-Hall distribution. Applying the torsion formulas to the BCOV invariant yields a computable obstruction to birational smooth fillings. For isolated singularities, its local contribution is expressed in terms of Hertling's spectral variance and a Bernoulli sum determined by monodromy. As applications, we rule out birational smooth fillings for projective Calabi-Yau degenerations with smooth total space and singular central fiber having only ADE or terminal Brieskorn-Pham singularities, in relative dimension at least three, extending results of Voisin.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12849",
  "author_total": 2,
  "authors": [
    {
      "name": "Dennis Eriksson"
    },
    {
      "name": "Gerard Freixas Montplet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcrac00y3khwh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12849",
  "fulltext_url": null,
  "id": "dcrac00y3khwh",
  "issns": [],
  "landing_url": "https://hal.science/hal-05796659v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "hal",
      "0.math"
    ]
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05796659/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcrac00y3khwh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:55Z",
      "native_id": "hal-05796659",
      "source": "hal",
      "url": "https://hal.science/hal-05796659v1"
    },
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12849",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12849"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "SPECTRUM OF SINGULARITIES, ANALYTIC TORSION AND CALABI-YAU DEGENERATIONS",
  "title_text": "SPECTRUM OF SINGULARITIES, ANALYTIC TORSION AND CALABI-YAU DEGENERATIONS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/dcrac00y3khwh",
  "venue": "HAL",
  "versions": []
}