2022/06/24 by Emilio Franco, Franco, Emilio, Robert Hanson +3
Arts and Humanities · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Caribbean and African Literature and Culture #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2206.12349
openalex publication_date 2022/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a finite covering β: C → X of a smooth projective curve X by a reduced, projective, planar curve C. Associated to two general polarizations on C, q and q', one can construct the corresponding compactified Prym varieties Pβ(q) and Pβ(q'). Consider Γ to be the group of line bundles whose torsion coincides with the order of β. In this article we construct a Fourier-Mukai transform between the derived categories of Pβ(q) and the Γ-equivariant derived category of Pβ(q'). Hence, we obtain a derived equivalence between the SL(n,ℂ)-Hitchin fibre and its associated PGL(n,ℂ)-Hitchin fibre for a dense class of singular spectral curves. Our work then provides the extension of the Fourier-Mukai transform constructed by Arinkin and Melo-Rapagnetta-Viviani, which corresponds to autoduality of GL(n,ℂ)-Hitchin fibres in this class of singular spectral curves.