Algebraic and Geometric Topology 5 (2005), paper no. 28, pages 691-711.

Some analogs of Zariski's Theorem on nodal line arrangements

A.D.R. Choudary, A. Dimca and S. Papadima

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

AMS subject classification. Primary: 32S22, 55N25. Secondary: 14F35, 52C35, 55Q52.

E-print: arXiv:math.AT/0410363

DOI: 10.2140/agt.2005.5.691

Submitted: 18 October 2004. (Revised: 12 May 2005.) Accepted: 27 June 2005. Published: 5 July 2005.

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A.D.R. Choudary, A. Dimca and S. Papadima
Department of Mathematics, Central Washington University
Ellensburg, Washington 98926, USA and
School of Mathematical Sciences, GC University Lahore, Pakistan

Laboratoire J.A. Dieudonne, UMR du CNRS 6621
Universite de Nice-Sophia-Antipolis, Parc Valrose
06108 Nice Cedex 02, France
and
Inst. of Math. "Simion Stoilow", P.O. Box 1-764, RO-014700 Bucharest, Romania

Email: choudary@cwu.edu, dimca@math.unice.fr, Stefan.Papadima@imar.ro

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