Addition theorems for Ziegler pairs of hyperplane arrangements

2025/09/23 by Takuro Abe, Abe, Takuro, Lukas Kühne +3
Mathematics · #13D02 #52C35 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2509.19011

openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by Terao's freeness conjecture, we examine Ziegler pairs, which are pairs of hyperplane arrangements that share the same underlying matroid but have different modules of logarithmic derivations. In this paper, we present a general construction that yields the first known families of Ziegler pairs in arbitrary dimension and size, starting from examples in the complex projective plane.

Citations

• Lorentzian polynomials and matroids over triangular hyperfields 1: Topological aspects
• A new hierarchy for complex plane curves
• On the numerical Terao's conjecture and Ziegler pairs for line arrangements
• Singular plane curves: freeness and combinatorics
• From Pascal's Theorem to the geometry of Ziegler's line arrangements
• Singular matroid realization spaces
• Addition-deletion theorems for the Solomon-Terao polynomials and B-sequences of hyperplane arrangements
• Geometric aspects of the Jacobian of a hyperplane arrangement
• Degeneration of pole order spectral sequences for hyperplane arrangements of 4 variables
• Elementary modifications and line configurations in P²

Related

• On the numerical Terao's conjecture and Ziegler pairs for line arrangements
• Projective dimensions of hyperplane arrangements
• Geometry of logarithmic derivations of hyperplane arrangements
• On Ziegler's conjectures for logarithmic derivations of arrangements
• Examples of strong Ziegler pairs of conic-line arrangements of degree 7 and 8