  Let $f: \CN \rightarrow \C $ be a reduced polynomial map, with $D=f^{-1}(0)$,
$\U=\CN \setminus D$ and boundary manifold $M=\partial \U$. Assume that $f$ is
transversal at infinity and $D$ has only isolated singularities. Then the only
interesting non-trivial Alexander modules of $\U$ and resp. $M$ appear in the
middle degree $n$. We revisit the mixed Hodge structures on these Alexander
modules and study their associated spectral pairs (or equivariant mixed Hodge
numbers). We obtain upper bounds for the spectral pairs of the $n$-th Alexander
module of $\U$, which can be viewed as a Hodge-theoretic refinement of
Libgober's divisibility result for the corresponding Alexander polynomials. For
the boundary manifold $M$, we show that the spectral pairs associated to the
non-unipotent part of the $n$-th Alexander module of $M$ can be computed in
terms of local contributions (coming from the singularities of $D$) and
contributions from "infinity".
