Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram.

We complete the construction of the fundamental diagram of various partial compactifications of themoduli spaces of mixedHodge structures with polarized graded quotients. The diagram includes the space of nilpotent orbits, the space of SL(2)-orbits, and the space of Borel-Serre orbits.We give amplifications of this fundamental diagram and amplify the relations of these spaces.We describe how this work is useful in understanding asymptotic behaviors of Beilinson regulators and of local height pairings in degeneration.We discuss mild degenerations in which regulators converge. [ABSTRACT FROM AUTHOR]