Maximal twisted Betti numbers of complex hyperplane arrangement complements

2025/11/11 by Yongqiang Liu, Liu, Yongqiang, Laurenţiu Maxim +3
Computer Science · Mathematics · #32S22 #32S60 #52C35 #55N25 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2511.08787

openalex publication_date 2025/11/11 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28

Abstract

We show that the Betti numbers of a local system on the complement of an essential complex hyperplane arrangement are maximized precisely when the local system is constant. This result answers positively a recent question of Yoshinaga and the first author.

Citations

• Maximal Betti number for local system cohomology of hyperplane arrangement complements
• Constructible sheaf complexes in complex geometry and Applications
• Morse theory, Milnor fibers and minimality of hyperplane arrangements

Related

• Maximal Betti number for local system cohomology of hyperplane arrangement complements
• Length of Perverse Sheaves on Hyperplane Arrangements
• The Universality of the Resonance Arrangement and its Betti Numbers
• Extremal Betti numbers of Rips complexes
• Morse theory, Milnor fibers and minimality of hyperplane arrangements