Hyperplane arrangements and Lefschetz's hyperplane section theorem

Details Hyperplane arrangements and Lefschetz's hyperplane section theorem Hyperplane arrangements and Lefschetz's hyperplane section theorem

2005-07-15

arxiv.org/abs/math/0507311v5

Kodai Math. Journal 30 no. 2 (2007) 157--194.

Mathematics

Algebraic Geometry

47 pages, 13 figures; v.2: typos corrected, references added, v.3: minor change, v.4: minor change, v.5: final form to appear

Scientific paper

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.

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