AbstractLet X be a projective manifold. The Hitchin morphism is a map from the moduli stack of Higgsbundles over X to the Hitchin base, which sends a Higgs bundle to its characteristic polynomial. lfX is a curve, it is well-known that the Hitchin morphism is surjective and it plays an important rolein the study of the moduli space of Higgs bundles. However, if X has dimension at least two, theH...
AbstractIn this talk, we will focus on Sp/SO Hitchin systems on marked curves with residues of Higgsfields lying in special nilpotent orbit closures which are related by the Springer correspondence. Wewill first show how to resolve singularities of generic spectral curves using Spaltenstein'sdescription of Kazhdan-Lusztig maps for classical groups via characteristic polynomials. Then wewill dis...