Algebraic & Geometric Topology

Some analogs of Zariski's Theorem on nodal line arrangements

A D Raza Choudary, Alexandru Dimca, and Ştefan Papadima

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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.

Article information

Algebr. Geom. Topol., Volume 5, Number 2 (2005), 691-711.

Received: 18 October 2004
Revised: 12 May 2005
Accepted: 27 June 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32S22: Relations with arrangements of hyperplanes [See also 52C35] 55N25: Homology with local coefficients, equivariant cohomology
Secondary: 14F35: Homotopy theory; fundamental groups [See also 14H30] 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 55Q52: Homotopy groups of special spaces

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


Choudary, A D Raza; Dimca, Alexandru; Papadima, Ştefan. Some analogs of Zariski's Theorem on nodal line arrangements. Algebr. Geom. Topol. 5 (2005), no. 2, 691--711. doi:10.2140/agt.2005.5.691.

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