Moduli stacks of Higgs bundles on stable curves

Abstract We construct a flat degeneration of the derived moduli stack of Higgs bundles on smooth projective curves, using Jun Li’s stack of bounded expanded degenerations. The degeneration carries a natural relative zero-shifted logarithmic symplectic form over the base, which extends the classical Hitchin symplectic structure from the generic fibre. The induced Hitchin map is shown to be complete (in the valuative sense) and flat, without requiring coprimeness of rank and degree. Finally, we extend the construction globally: the derived moduli stack of Higgs bundles over the universal semistable curve of genus greater than or equal to two carries a relative zero-shifted log-symplectic form over the moduli stack of stable curves.