Hyperplane arrangements and Lefschetz's hyperplane section theorem

Masahiko Yoshinaga

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Hyperplane arrangements and Lefschetz's hyperplane section theorem

Masahiko Yoshinaga

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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.

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BibTeX RIS

Masahiko Yoshinaga. 2005-07-15. Hyperplane arrangements and Lefschetz's hyperplane section theorem. https://arxiv.org/abs/math/0507311

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