  We investigate the interplay between the monodromy and the Deligne mixed
Hodge structure on the Milnor fiber of a homogeneous polynomial. In the case of
hyperplane arrangement Milnor fibers, we obtain a new result on the possible
weights. For line arrangements, we prove in a new way the fact due to Budur and
Saito that the spectrum is determined by the weak combinatorial data, and show
that such a result fails for the Hodge-Deligne polynomials.
