{
  "abstract": "For every nonempty Hassett divisor $\\mathcal C_d$ parameterizing special cubic fourfolds, we consider the quaternion class $β_d=(d/2,-3)$ in the two-torsion Brauer group. We prove that if a Hodge-general member of ${C}_d$ is rational then $β_d=0$ -- or, equivalently, that Huybrechts' twisted-K3 condition $(**')$ holds. Consequently, a very general member of $\\mathcal C_d$ is irrational if $β_d\\ne0$. Thus, a very general cubic fourfold containing a smooth cubic scroll or a Veronese surface is irrational, and hence so is a very general Küchle fourfold of type $(\\mathrm{c7})$. We also obtain an analogous obstruction for Hodge--special Gushel--Mukai fourfolds: a very general member in the discriminant--$d$ locus can be rational only if $d$ is a sum of two squares. Consequently, a very general Gushel--Mukai fourfold containing a cubic scroll is irrational.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06759",
  "author_total": 1,
  "authors": [
    {
      "name": "Aideen Fay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/056wng65k2xtx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06759",
  "fulltext_url": null,
  "id": "056wng65k2xtx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06759",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212022276",
  "pdf_url": "https://arxiv.org/pdf/2609.06759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/056wng65k2xtx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hasse Obstructions to Rationality for Special Fourfolds",
  "title_text": "Hasse Obstructions to Rationality for Special Fourfolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/056wng65k2xtx",
  "venue": "arXiv",
  "versions": []
}