Hyperplane arrangements and Lefschetz's hyperplane section theorem
By Masahiko Yoshinaga. 2005
47 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b71b0004f42bdc37574231c48807a18aed6f483a
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Combinatorial Morse theory and minimality of hyperplane arrangements (2007, methodology): “The existence of such minimal complex was proved before Dimca and Padadima [5] and Randell [14] and there exists also some description of it by Yoshinaga [19].”