论文标题
校长的权力$ q $ - 伯雷尔理想
Powers of Principal $Q$-Borel ideals
论文作者
论文摘要
修复$ \ {x_1，\ ldots，x_n \} $上的poset $ q $。 a $ q $ -borel单一理想$ i \ subseteq \ mathbb {k} [x_1，\ ldots，x_n] $是一个单一理想的理想，其单元在像$ q $的borel样动作下关闭。单一理想$ i $是主要的$ q $ - borel理想，表示为$ i = q（m）$，如果有单个$ m $，以便可以通过$ m $ $ m $的$ q $ borel移动获得所有最小的$ i $的发电机。在本文中，我们研究了本金$ q $ -borel理想的权力。在我们的结果中，我们表明，$ Q（m）$的所有权力都符合其象征力量，并且理想的$ q（m）$满足了相关素数的持久性属性。我们还根据poset $ q $计算$ q（m）$的分析价差。
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 $Q$.
