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PreprintCC BY 4.0arXiv

Fourier duality on compactified Prym fibrations

  • Anne Larsen
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Abstract

We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of 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.

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Cite

BibTeXRIS
BibTeX
@misc{larsen2026fourier,
  title = {{Fourier duality on compactified Prym fibrations}},
  author = {Anne Larsen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31604},
  eprint = {2609.31604},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31604},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fourier duality on compactified Prym fibrations
AU  - Anne Larsen
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31604
UR  - https://arxiv.org/abs/2609.31604
AB  - We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of 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.
ER  -