The $\text{v}$-function of powers of sums of ideals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912012062162944 |
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| author | Ficarra, Antonino Marques, Pedro Macias |
| author_facet | Ficarra, Antonino Marques, Pedro Macias |
| contents | Let $K$ be a field, $I\subset R=K[x_1,\dots,x_n]$ and $J\subset T=K[y_1,\dots,y_m]$ be graded ideals. Set $S=R\otimes_KT$ and let $L=IS+JS$. The behaviour of the $\text{v}$-function $\text{v}(L^k)$ in terms of the $\text{v}$-functions $\text{v}(I^k)$ and $\text{v}(J^k)$ is investigated. When $I$ and $J$ are monomial ideals, we describe $\text{v}(L^k)$, giving an explicit formula involving $\text{v}(I^k)$ and $\text{v}(J^k)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $\text{v}$-function of powers of sums of ideals Ficarra, Antonino Marques, Pedro Macias Commutative Algebra Combinatorics Let $K$ be a field, $I\subset R=K[x_1,\dots,x_n]$ and $J\subset T=K[y_1,\dots,y_m]$ be graded ideals. Set $S=R\otimes_KT$ and let $L=IS+JS$. The behaviour of the $\text{v}$-function $\text{v}(L^k)$ in terms of the $\text{v}$-functions $\text{v}(I^k)$ and $\text{v}(J^k)$ is investigated. When $I$ and $J$ are monomial ideals, we describe $\text{v}(L^k)$, giving an explicit formula involving $\text{v}(I^k)$ and $\text{v}(J^k)$. |
| title | The $\text{v}$-function of powers of sums of ideals |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2405.16882 |