# A question on Steenbrink's paper, limit of Hodge structures

Steenbrink in his paper "Limit of Hodge Structures", (supplemented by the book "Mixed Hodge Structures" by Peters and Steenbrink) discuss the limit mixed Hodge structures for a fibration over the unit disc $\Delta \subset \mathbb{C}$, i.e. a fibration $$\pi: X \rightarrow \Delta$$ whose fibers are projective varieties and the only singular fiber is over 0, which is a reduced divisor with smooth normal crossing components.

Question: Does Steenbrink's construction in his paper (or book) work in the general case i.e. for a fibration $$\pi: X \rightarrow \Delta^n$$ I guess this also involves the issues with "simultaneous semi-stable reduction" of this family, which has been discussed in the paper "A tour of stable reduction with applications".

If $\pi$ is semistable, then Fujisawa, Limits of Hodge structures in several variables. Compositio (1999), does this. You might also look at some later papers by the same author for some refinements.