Some analogs of Zariski's Theorem on nodal line arrangements

Authors

A.D. Raza Choudary, Central Washington UniversityFollow
Alexandru Dimca, Université de Nice-Sophia-Antipolis
Ştefan Papadima, Simion Stoilow Institute of Mathematics of the Romanian Academy

Department or Administrative Unit

Mathematics

Document Type

Article

Author Copyright

© Geometry & Topology Publications

Publication Date

7-5-2005

Journal

Algebraic & Geometric Topology

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.

Comments

This article was originally published in Algebraic & Geometric Topology. The full-text article from the publisher can be found here.

Recommended Citation

Choudary, A. D. R., Dimca, A., & Papadima, T. (2005). Some analogs of Zariski’s Theorem on nodal line arrangements. Algebraic & Geometric Topology, 5(2), 691–711. https://doi.org/10.2140/agt.2005.5.691