{
  "abstract": "We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of $\\mathrm{SL}$ Higgs bundles over the elliptic locus. This leads to a shadow of the Hausel-Thaddeus conjecture, proof of the Corti-Hanamura motivic decomposition conjecture for these fibrations, and multiplicativity of the perverse filtration. Our approach can be described as a generalization of the Maulik-Shen-Yin package for compactified Jacobian fibrations to the case when the dual abelian fibration is a stack. This forces us to move beyond the case of full supports. Technical tools include a new pullback identity for the stacky Grothendieck-Riemann-Roch tau functor introduced by Toën, results on descent of (Arinkin-)Poincaré sheaves, and a comparison of Poincaré sheaves of the Prym varieties of families of smooth and nodal curves along the lines of Franco-Hanson-Horn-Oliveira.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31604",
  "author_total": 1,
  "authors": [
    {
      "name": "Anne Larsen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abq51vegnamqz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31604",
  "fulltext_url": null,
  "id": "abq51vegnamqz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31604",
  "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": "W7214675432",
  "pdf_url": "https://arxiv.org/pdf/2609.31604",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abq51vegnamqz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31604",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31604"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fourier duality on compactified Prym fibrations",
  "title_text": "Fourier duality on compactified Prym fibrations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/abq51vegnamqz",
  "venue": "arXiv",
  "versions": []
}