Alexander invariants of complex hyperplane arrangements

Let be an arrangement of complex hyperplanes. The fundamental group of the complement of is determined by a braid monodromy homomorphism, . Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of . From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of . We also provide a combinatorial criterion for when these lower bounds are attained.