Some analogs of Zariski’s Theorem on nodal line arrangements

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.

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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

Volume 5, issue 2 (2005)

A D Raza Choudary, Alexandru Dimca and Ştefan Papadima

Abstract