  Let $V$ be a degree $d$, reduced hypersurface in $\mathbb{CP}^{n+1}$, $n \geq
1$, and fix a generic hyperplane, $H$. Denote by $\mathcal{U}$ the (affine)
hypersurface complement, $\mathbb{CP}^{n+1}- V \cup H$, and let $\mathcal{U}^c$
be the infinite cyclic covering of $\mathcal{U}$ corresponding to the kernel of
the linking number homomorphism. Using intersection homology theory, we give a
new construction of the Alexander modules $H_i(\mathcal{U}^c;\mathbb{Q})$ of
the hypersurface complement and show that, if $i \leq n$, these are torsion
over the ring of rational Laurent polynomials. We also obtain obstructions on
the associated global polynomials. Their zeros are roots of unity of order $d$
and are entirely determined by the local topological information encoded by the
link pairs of singular strata of a stratification of the pair
$(\mathbb{CP}^{n+1},V)$. As an application, we give obstructions on the
eigenvalues of monodromy operators associated to the Milnor fibre of a
projective hypersurface arrangement.
