Kodai Mathematical Journal

Hyperplane arrangements and Lefschetz's hyperplane section theorem

Masahiko Yoshinaga

Full-text: Open access

Abstract

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.

Article information

Source
Kodai Math. J., Volume 30, Number 2 (2007), 157-194.

Dates
First available in Project Euclid: 3 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1183475510

Digital Object Identifier
doi:10.2996/kmj/1183475510

Mathematical Reviews number (MathSciNet)
MR2343416

Zentralblatt MATH identifier
1142.32012

Citation

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


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