Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Larsen, Anne
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214675432