The Hitchin morphism for K-trivial varieties

We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the spectral base. In other words, a stronger version of the conjecture of Chen and Ngô holds for this class of varieties, which includes K-trivial varieties. As part of the proof, we slightly modify the construction of spectral covers to obtain normal spectral covers.