Volume 5, issue 2 (2005)

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Some analogs of Zariski's Theorem on nodal line arrangements

A D Raza Choudary, Alexandru Dimca and Ştefan Papadima

Algebraic & Geometric Topology 5 (2005) 691–711
 arXiv: math.AT/0410363
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.

Keywords
hyperplane arrangement, oriented topological type, 1–marked group, intersection lattice, local system, Milnor fiber, Alexander cover
Mathematical Subject Classification 2000
Primary: 32S22, 55N25
Secondary: 14F35, 52C35, 55Q52