Homology of Local Systems on Real Line Arrangement Complements

2025/12/25 by Baiting Xie, Chenglong Yu, Xie, Baiting +1
Computer Science · Mathematics · #32S22 (Primary) 14N20 #52C35 #55N25 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2512.21531

openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real figures of the arrangement. It enables us to give a new upper bound. We further consider the case where the arrangement contains a sharp pair and make partial progress on a conjecture proposed by Yoshinaga.

Citations

• Topology and combinatorics of real line arrangements

Related

• Admissible local systems for a class of line arrangements
• Arrangements and local systems
• Cohomology of ℤ-local systems on complex hyperplane arrangement complements
• Topological line arrangements and their topological invariants
• Semi-algebraic partition and basis of Borel-Moore homology of hyperplane arrangements