Resonance varieties and Lie algebras of matroids and hyperplane arrangements
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912613230706688 |
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| author | Suciu, Alexandru |
| author_facet | Suciu, Alexandru |
| contents | The resonance varieties, the holonomy Lie algebra, and the holonomy Chen Lie algebra associated with the Orlik-Solomon algebra of a matroid provide an algebraic lens through which to examine the rich combinatorial structure of matroids and their geometric realizations as complex hyperplane arrangements. In this survey paper, we emphasize the commonalities between these objects but also the possible ways in which realizable and non-realizable matroids differ, leading to some open questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resonance varieties and Lie algebras of matroids and hyperplane arrangements Suciu, Alexandru Combinatorics Algebraic Geometry 52C35, 14N20, 16W70, 17B70, 20F14, 20F40, 52B40, 57M07 The resonance varieties, the holonomy Lie algebra, and the holonomy Chen Lie algebra associated with the Orlik-Solomon algebra of a matroid provide an algebraic lens through which to examine the rich combinatorial structure of matroids and their geometric realizations as complex hyperplane arrangements. In this survey paper, we emphasize the commonalities between these objects but also the possible ways in which realizable and non-realizable matroids differ, leading to some open questions. |
| title | Resonance varieties and Lie algebras of matroids and hyperplane arrangements |
| topic | Combinatorics Algebraic Geometry 52C35, 14N20, 16W70, 17B70, 20F14, 20F40, 52B40, 57M07 |
| url | https://arxiv.org/abs/2509.24060 |