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arXiv · 2305.06835

On binomial complete intersections

Filip Jonsson Kling·Samuel Lundqvist·Lisa Nicklasson
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Abstract

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.

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Filip Jonsson Kling, Samuel Lundqvist, Lisa Nicklasson. 2024-03-22. On binomial complete intersections. https://arxiv.org/abs/2305.06835

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