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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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
References
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Publication
Received: 18 October 2004
Revised: 12 May 2005
Accepted: 27 June 2005
Published: 5 July 2005
Authors
A D Raza Choudary
Department of Mathematics
Central Washington University
Ellensburg
Washington 98926
USA
School of Mathematical Sciences
GC University
Lahore
Pakistan
Alexandru Dimca
Laboratoire J.A. Dieudonné
UMR du CNRS 6621
Université de Nice-Sophia-Antipolis
Parc Valrose
06108 Nice Cedex 02
France
Ştefan Papadima
Inst. of Math. “Simion Stoilow"
P.O. Box 1-764
RO-014700 Bucharest, Romania