Generic Fibers of Parabolic Hitchin Maps: $GL_{n}$-Case

In this talk, we will discuss parabolic Hitchin maps over algebraic curves and their generic fibers. The main result is a parabolic analogue of the Beauville–Narasimhan–Ramanan’s correspondence which is proved via a detailed study of both geometric and algebraic structures of generic singular spectral curves. In particular, it shows that generic fibers are Picard varieties of normalized spectral curves. If time permits, we will also discuss the parabolic global nilpotent cones. This is a joint work with Xiaoyu Su and Xueqing Wen.