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arXiv · 2509.19011

Addition theorems for Ziegler pairs of hyperplane arrangements

Takuro Abe·Lukas Kühne·Piotr Pokora
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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.

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Takuro Abe, Lukas Kühne, Piotr Pokora. 2026-06-10. Addition theorems for Ziegler pairs of hyperplane arrangements. https://arxiv.org/abs/2509.19011

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