Complex structures on partial compactifications of arithmetic quotients of classifying spaces of Hodge structures (Q1902884)

We construct partial compactification of arithmetic quotients of the classifying spaces of polarized Hodge structures of general weight by adding the restrictions of the `tamest' nilpotent orbits to the invariant cycles, and introduce complex structures on them. We prove holomorphic extendability of period maps from a puctured disc whose monodromy logarithm satisfies a certain property. We also examine some geometric examples which can be settled within the present framework.