Some analogs of Zariski’s Theorem on nodal line arrangements

Choudary, A D Raza¹ ; Dimca, Alexandru² ; Papadima, Ştefan³

¹Department of Mathematics, Central Washington University, Ellensburg, Washington 98926, USA, School of Mathematical Sciences, GC University, Lahore, Pakistan
²Laboratoire J.A. Dieudonné, UMR du CNRS 6621, Université de Nice-Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
³Inst. of Math. “Simion Stoilow", P.O. Box 1-764, RO-014700 Bucharest, Romania

Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 691-711

Résumé

For line arrangements in ℙ2 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.

Détail

DOI : 10.2140/agt.2005.5.691

Keywords: hyperplane arrangement, oriented topological type, 1–marked group, intersection lattice, local system, Milnor fiber, Alexander cover

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