For line arrangements in
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.
Keywords
hyperplane arrangement, oriented topological type, 1–marked
group, intersection lattice, local system, Milnor fiber,
Alexander cover