Some analogs of Zariski's Theorem on nodal line arrangements

Abstract

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-28.abs.html

References in corpus (1)

• Torsion in Milnor fiber homology

Cited by in corpus (4)

• Characterization of Line Arrangement for which the Fundamental Group of the Complement is a Direct Product of Free Groups
• Milnor fibrations of arrangements with trivial algebraic monodromy
• Line arrangements and direct sums of free groups
• Admissibility of local systems for some classes of line arrangements