Classifying spaces of degenerating mixed Hodge structures. III: Spaces of nilpotent orbits (Q2857296)

In this paper the results of \textit{K. Kato} and \textit{S. Usui} [Classifying spaces of degenerating polarized Hodge structures. Annals of Mathematics Studies 169. Princeton, NJ: Princeton University Press (2009; Zbl 1172.14002)] are generalized to the mixed Hodge-theoretic context. This is Part III of the series of papers by the authors studying degeneration of mixed Hodge structures. In this part the authors construct toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients, study their properties, and prove that they are moduli spaces of log mixed Hodge structures with polarized graded quotients. They are constructed as the spaces of nilpotent orbits. The obtained results are applied to investigating Néron models including degenerations of intermediate Jacobians.