Separator-based derivations of graphic arrangements
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916710278234112 |
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| author | Mühlherr, Leonie |
| author_facet | Mühlherr, Leonie |
| contents | The class of subarrangements of the well-studied braid arrangement, so-called graphic hyperplane arrangements, is important for analysing new concepts and properties in hyperplane arrangement theory. While there is a nice characterization of free graphic arrangements, many interesting questions beyond the free case remain open. This paper introduces an explicit set of generators for the module of logarithmic derivations of a general graphic arrangement based on graph separators. We obtain new insights in the derivation degree sequence in the non-free case and give bounds on the highest degree in the sequence. Moreover, this can broadly be used for future research in this area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separator-based derivations of graphic arrangements Mühlherr, Leonie Combinatorics Commutative Algebra 52C35, 32S22, 13N15, 05C40 The class of subarrangements of the well-studied braid arrangement, so-called graphic hyperplane arrangements, is important for analysing new concepts and properties in hyperplane arrangement theory. While there is a nice characterization of free graphic arrangements, many interesting questions beyond the free case remain open. This paper introduces an explicit set of generators for the module of logarithmic derivations of a general graphic arrangement based on graph separators. We obtain new insights in the derivation degree sequence in the non-free case and give bounds on the highest degree in the sequence. Moreover, this can broadly be used for future research in this area. |
| title | Separator-based derivations of graphic arrangements |
| topic | Combinatorics Commutative Algebra 52C35, 32S22, 13N15, 05C40 |
| url | https://arxiv.org/abs/2504.19893 |