Componentwise Linear Ideals From Sums
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909569489305600 |
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| author | Dao, Hailong Suresh-Babu, Sreehari |
| author_facet | Dao, Hailong Suresh-Babu, Sreehari |
| contents | Let $I,J$ be componentwise linear ideals in a polynomial ring $S$. We study necessary and sufficient conditions for $I+J$ to be componentwise linear. We provide a complete characterization when $\dim S=2$. As a consequence, any componentwise linear monomial ideal in $k[x,y]$ has linear quotients using generators in non-decreasing degrees. In any dimension, we show that under mild compatibility conditions, one can build a componentwise linear ideal from a given collection of componentwise linear monomial ideals using only sum and product with square-free monomials. We provide numerous examples to demonstrate the optimality of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Componentwise Linear Ideals From Sums Dao, Hailong Suresh-Babu, Sreehari Commutative Algebra Combinatorics Let $I,J$ be componentwise linear ideals in a polynomial ring $S$. We study necessary and sufficient conditions for $I+J$ to be componentwise linear. We provide a complete characterization when $\dim S=2$. As a consequence, any componentwise linear monomial ideal in $k[x,y]$ has linear quotients using generators in non-decreasing degrees. In any dimension, we show that under mild compatibility conditions, one can build a componentwise linear ideal from a given collection of componentwise linear monomial ideals using only sum and product with square-free monomials. We provide numerous examples to demonstrate the optimality of our results. |
| title | Componentwise Linear Ideals From Sums |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2504.05261 |