  For line arrangements in P^2 with nice combinatorics (in particular, for
those which are nodal away the line at infinity), we prove that the
combinatorics contains the same information as the fundamental group together
with the meridianal basis of the abelianization. We consider higher dimensional
analogs of the above situation. For these analogs, we give purely combinatorial
complete descriptions of the following topological invariants (over an
arbitrary field): the twisted homology of the complement, with arbitrary rank
one coefficients; the homology of the associated Milnor fiber and Alexander
cover, including monodromy actions; the coinvariants of the first higher
non-trivial homotopy group of the Alexander cover, with the induced monodromy
action.
