2023/12/09 by Klingner, Tyson · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.05711
We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the SO2n+1-Hitchin fibration where the Higgs fields are L-twisted endomorphisms. Although the spectral data is known in the literature, we develop a new approach to spectral data, which takes advantage of Hecke modification. Further, we present the computation for the Sp2n and SO2n cases while clarifying some aspects of the correspondence which are not well explained in the pre-existing literature. We also compute the number of connected components of the generic fibres, and demonstrate Langlands duality in the fibres via the canonical duality in the fibres.