论文标题
单一理想的Klyachko图
Klyachko diagrams of monomial ideals
论文作者
论文摘要
在本文中，我们介绍了在某些多级多项式戒指中的单一理想$ i $的Klyachko图的概念，即平滑完整的复合品种的Cox Rug $ r $，具有无关的最大理想$ b $。我们介绍了从其单体发电机中计算$ i $的Klyachko图，并从其Klyachko图中检索$ b- $饱和$ i^{\ mathrm {sat}} $ $ i $的$。我们使用此描述来计算第一个本地共同体模块$ h^{1} _ {b}（i）$。作为一个应用程序，我们找到了$ i^{\ mathrm {sat}} $的希尔伯特功能的公式，以及用klyachko图来表征具有恒定希尔伯特多项式的单一理想。
In this paper, we introduce the notion of a Klyachko diagram for a monomial ideal $I$ in a certain multi-graded polynomial ring, namely the Cox ring $R$ of a smooth complete toric variety, with irrelevant maximal ideal $B$. We present procedures to compute the Klyachko diagram of $I$ from its monomial generators, and to retrieve the $B-$saturation $I^{\mathrm{sat}}$ of $I$ from its Klyachko diagram. We use this description to compute the first local cohomology module $H^{1}_{B}(I)$. As an application, we find a formula for the Hilbert function of $I^{\mathrm{sat}}$, and a characterization of monomial ideals with constant Hilbert polynomial, in terms of their Klyachko diagram.
