  We show that the KZ system has a purely topological interpretation in the
sense that it may be understood as a variation of complex mixed Hodge structure
whose successive pure weight quotients are polarized. This in a sense completes
and elucidates work of Schechtman-Varchenko done in the early 1990's. A central
ingredient is a new realization of the irreducible highest weight
representations of a Lie algebra of Kac-Moody type, namely on an algebra of
rational polydifferentials on a countable product of Riemann spheres.
