Artinian Gorenstein algebras with binomial Macaulay dual generator
Fuente:
arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910843875098624 |
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| author | Altafi, Nasrin Dinu, Rodica Faridi, Sara Masuti, Shreedevi K. Miró-Roig, Rosa M. Seceleanu, Alexandra Villamizar, Nelly |
| author_facet | Altafi, Nasrin Dinu, Rodica Faridi, Sara Masuti, Shreedevi K. Miró-Roig, Rosa M. Seceleanu, Alexandra Villamizar, Nelly |
| contents | This paper initiates a systematic study for key properties of Artinian Gorenstein \(K\)-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all such algebras satisfy the strong Lefschetz property, can be constructed as a doubling of an appropriate 0-dimensional scheme in \(\mathbb{P}^2\), and we provide an explicit characterization of when they form a complete intersection. For arbitrary codimension, we establish sufficient conditions under which the weak Lefschetz property holds and show that these conditions are optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Artinian Gorenstein algebras with binomial Macaulay dual generator Altafi, Nasrin Dinu, Rodica Faridi, Sara Masuti, Shreedevi K. Miró-Roig, Rosa M. Seceleanu, Alexandra Villamizar, Nelly Commutative Algebra This paper initiates a systematic study for key properties of Artinian Gorenstein \(K\)-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all such algebras satisfy the strong Lefschetz property, can be constructed as a doubling of an appropriate 0-dimensional scheme in \(\mathbb{P}^2\), and we provide an explicit characterization of when they form a complete intersection. For arbitrary codimension, we establish sufficient conditions under which the weak Lefschetz property holds and show that these conditions are optimal. |
| title | Artinian Gorenstein algebras with binomial Macaulay dual generator |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2502.18149 |