Birational invariance conjecture for the image of the Hitchin morphism

Let $X$ and $Y$ be smooth proper varieties related by a smooth birational modification, and let $h^r_X$ and $h^r_Y$ denote their Hitchin morphisms. Their spectral bases are identified by the induced birational pullback.

Birational invariance conjecture. The set-theoretic image $\operatorname{im}(h^r_X)$ of the Hitchin morphism is invariant under smooth birational modifications.

This is presented as an equivalent reformulation of the Chen–Ngô surjectivity conjecture. The paper proves invariance of the spectral base under smooth birational modifications, while invariance of the set-theoretic Hitchin image remains open in general.