Hyperplane arrangements and Lefschetz's hyperplane section theorem
Algebraic Geometry
2011-11-10 v5 Algebraic Topology
Combinatorics
Geometric Topology
Abstract
The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these cells for the complement of a complex hyperplane arrangement defined over real numbers. The cells and attaching maps are described in combinatorial terms of chambers. We also discuss the cellular chain complex with coefficients in a local system and a presentation for the fundamental group associated to the minimal CW-decomposition for the complement.
Cite
@article{arxiv.math/0507311,
title = {Hyperplane arrangements and Lefschetz's hyperplane section theorem},
author = {Masahiko Yoshinaga},
journal= {arXiv preprint arXiv:math/0507311},
year = {2011}
}
Comments
47 pages, 13 figures; v.2: typos corrected, references added, v.3: minor change, v.4: minor change, v.5: final form to appear in Kodai Math. Journal (2007)