Kodai Mathematical Journal
- Kodai Math. J.
- Volume 30, Number 2 (2007), 157-194.
Hyperplane arrangements and Lefschetz's hyperplane section theorem
The Lefschetz hyperplane section theorem asserts that a complex 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 give an explicit description of 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.
Kodai Math. J., Volume 30, Number 2 (2007), 157-194.
First available in Project Euclid: 3 July 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Yoshinaga, Masahiko. Hyperplane arrangements and Lefschetz's hyperplane section theorem. Kodai Math. J. 30 (2007), no. 2, 157--194. doi:10.2996/kmj/1183475510. https://projecteuclid.org/euclid.kmj/1183475510