Limits of Hodge structures in several variables, II

Abstract

The aim of this article is to study degeneration of the variations of Hodge structure associated to a proper K\"ahler semistable morphism. We prove that the weight filtrations constructed in the author's previous paper coincide with the monodromy weight filtrations on the relative log de Rham cohomology groups of a proper K\"ahler semistable morphism. Moreover, we show that the limiting mixed Hodge structures form admissible variations of mixed Hodge structure.