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arXiv · 2105.07307

On the Waldschmidt constant of square-free principal Borel ideals

Eduardo Camps Moreno·Craig Kohne·Eliseo Sarmiento·Adam Van Tuyl
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Abstract

Fix a square-free monomial $m \in S = \mathbb{K}[x_1,\ldots,x_n]$. The square-free principal Borel ideal generated by $m$, denoted ${\rm sfBorel}(m)$, is the ideal generated by all the square-free monomials that can be obtained via Borel moves from the monomial $m$. We give upper and lower bounds for the Waldschmidt constant of ${\rm sfBorel}(m)$ in terms of the support of $m$, and in some cases, exact values. For any rational $\frac{a}{b} \geq 1$, we show that there exists a square-free principal Borel ideal with Waldschmidt constant equal to $\frac{a}{b}$.

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Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento, Adam Van Tuyl. 2021-05-15. On the Waldschmidt constant of square-free principal Borel ideals. https://arxiv.org/abs/2105.07307

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