Addition theorems for Ziegler pairs of hyperplane arrangements
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909802438852608 |
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| author | Abe, Takuro Kühne, Lukas Pokora, Piotr |
| author_facet | Abe, Takuro Kühne, Lukas Pokora, Piotr |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Addition theorems for Ziegler pairs of hyperplane arrangements Abe, Takuro Kühne, Lukas Pokora, Piotr Combinatorics Commutative Algebra Algebraic Geometry 52C35, 13D02 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. |
| title | Addition theorems for Ziegler pairs of hyperplane arrangements |
| topic | Combinatorics Commutative Algebra Algebraic Geometry 52C35, 13D02 |
| url | https://arxiv.org/abs/2509.19011 |