On binomial complete intersections
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914904623022080 |
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| author | Kling, Filip Jonsson Lundqvist, Samuel Nicklasson, Lisa |
| author_facet | Kling, Filip Jonsson Lundqvist, Samuel Nicklasson, Lisa |
| contents | We consider homogeneous binomial ideals $I=(f_1,\ldots,f_n)$ in $K[x_1, \ldots, x_n]$, where $f_i = a_i x_i^{d_i} - b_i m_i$ and $a_i \neq 0$. When such an ideal is a complete intersection, we show that the monomials which are not divisible by $x_i^{d_i}$ for $i=1,\ldots,n$ form a vector space basis for the corresponding quotient, and we describe the Macaulay dual generator in terms of a directed graph that we associate to $I$. These two properties can be seen as a natural generalization of well-known properties for monomial complete intersections. Moreover, we give a description of the radical of the resultant of $I$ in terms of the directed graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06835 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On binomial complete intersections Kling, Filip Jonsson Lundqvist, Samuel Nicklasson, Lisa Commutative Algebra 13C40, 13E10, 13F65, 13P15, 16S15 We consider homogeneous binomial ideals $I=(f_1,\ldots,f_n)$ in $K[x_1, \ldots, x_n]$, where $f_i = a_i x_i^{d_i} - b_i m_i$ and $a_i \neq 0$. When such an ideal is a complete intersection, we show that the monomials which are not divisible by $x_i^{d_i}$ for $i=1,\ldots,n$ form a vector space basis for the corresponding quotient, and we describe the Macaulay dual generator in terms of a directed graph that we associate to $I$. These two properties can be seen as a natural generalization of well-known properties for monomial complete intersections. Moreover, we give a description of the radical of the resultant of $I$ in terms of the directed graph. |
| title | On binomial complete intersections |
| topic | Commutative Algebra 13C40, 13E10, 13F65, 13P15, 16S15 |
| url | https://arxiv.org/abs/2305.06835 |