  We start with a discussion on Alexander invariants, and then prove some
general results concerning the divisibility of the Alexander polynomials and
the supports of the Alexander modules, via Artin's vanishing theorem for
perverse sheaves. We conclude with explicit computations of twisted cohomology
following an idea already exploited in the hyperplane arrangement case, which
combines the degeneration of the Hodge to de Rham spectral sequence to the
purity of some cohomology groups.
