## Algebraic & Geometric Topology

### Some analogs of Zariski's Theorem on nodal line arrangements

#### Abstract

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.

#### Article information

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

Dates
Revised: 12 May 2005
Accepted: 27 June 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796426

Digital Object Identifier
doi:10.2140/agt.2005.5.691

Mathematical Reviews number (MathSciNet)
MR2153112

Zentralblatt MATH identifier
1081.32018

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796426

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