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arXiv · 2010.13889

Powers of Principal $Q$-Borel ideals

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

Fix a poset $Q$ on $\{x_1,\ldots,x_n\}$. A $Q$-Borel monomial ideal $I \subseteq \mathbb{K}[x_1,\ldots,x_n]$ is a monomial ideal whose monomials are closed under the Borel-like moves induced by $Q$. A monomial ideal $I$ is a principal $Q$-Borel ideal, denoted $I=Q(m)$, if there is a monomial $m$ such that all the minimal generators of $I$ can be obtained via $Q$-Borel moves from $m$. In this paper we study powers of principal $Q$-Borel ideals. Among our results, we show that all powers of $Q(m)$ agree with their symbolic powers, and that the ideal $Q(m)$ satisfies the persistence property for associated primes. We also compute the analytic spread of $Q(m)$ in terms of the poset $Q$.

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Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento, Adam Van Tuyl. 2020-10-26. Powers of Principal $Q$-Borel ideals. https://arxiv.org/abs/2010.13889

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