Minimality of hyperplane arrangements and basis of local system cohomology

2010/02/10 by Masahiko Yoshinaga, Yoshinaga, Masahiko
Mathematics · #32S22 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1002.2038

openalex publication_date 2010/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top degree, and bounded chambers form a basis of the remaining cohomology group. We determine precisely when this phenomenon happens for two-dimensional arrangements.

Citations

• Higher Homotopy Groups of Complements of Complex Hyperplane Arrangements

Related

• Non-vanishing of the twisted cohomology on the complement of hypersurfaces
• β-nbc bases for cohomology of local systems on hyperplane complements
• Admissible local systems for a class of line arrangements
• Hyperplane arrangements, M-tame polynomials and twisted cohomology
• Rank one local systems on complements of hyperplanes and Aomoto complexes