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| Auteurs principaux: | , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2605.19880 |
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| _version_ | 1866911698507530240 |
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| author | Gaubatz, Nicholas Schenck, Hal |
| author_facet | Gaubatz, Nicholas Schenck, Hal |
| contents | In 1994, Orlik and Terao introduced a commutative Artinian analog S/I(A) of the Orlik-Solomon algebra of a hyperplane arrangement A to answer a question of Aomoto. A central topic of investigation in the study of Artinian algebras is the Weak Lefschetz Property (WLP). We analyze WLP for the Artinian Orlik-Terao algebra of graphc arrangements. Even for chordal graphs (which give rise to Koszul algebras) WLP sometimes fails; conversely an analysis of the state polytope shows WLP can hold even when WLP fails for all possible initial ideals. More generally, for any algebra with a tensor product decomposition, we construct canonical elements in the kernel of the multiplication map, refining previous results in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19880 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subarrangements of type A: the weak Lefschetz property of the Artinian Orlik-Terao algebra Gaubatz, Nicholas Schenck, Hal Commutative Algebra Combinatorics 13D02, 52C35, 13D40 In 1994, Orlik and Terao introduced a commutative Artinian analog S/I(A) of the Orlik-Solomon algebra of a hyperplane arrangement A to answer a question of Aomoto. A central topic of investigation in the study of Artinian algebras is the Weak Lefschetz Property (WLP). We analyze WLP for the Artinian Orlik-Terao algebra of graphc arrangements. Even for chordal graphs (which give rise to Koszul algebras) WLP sometimes fails; conversely an analysis of the state polytope shows WLP can hold even when WLP fails for all possible initial ideals. More generally, for any algebra with a tensor product decomposition, we construct canonical elements in the kernel of the multiplication map, refining previous results in the literature. |
| title | Subarrangements of type A: the weak Lefschetz property of the Artinian Orlik-Terao algebra |
| topic | Commutative Algebra Combinatorics 13D02, 52C35, 13D40 |
| url | https://arxiv.org/abs/2605.19880 |