Generalized parabolic Hitchin pairs

We define generalized parabolic Hitchin (GPH) pairs on a non‐singular curve X and construct their moduli spaces. When X is the normalization of an integral projective curve Y , we give a birational morphism from the moduli space of good GPH on X to the moduli space of Hitchin pairs on Y . We define a Hitchin map on GPH and show that it is a proper map on the moduli space of GPH and induces a proper Hitchin morphism on a subscheme of the moduli space of Hitchin pairs on Y . We study the relationship between Hitchin pairs and the compactified Jacobian of a spectral curve.