论文标题
单一理想的Valabrega-Valla模块
The Valabrega-Valla modules of monomial ideals
论文作者
论文摘要
在本文中，我们专注于一对单一理想的Valabrega-valla模块的初始学位和消失，$ j \ subseteq i $ $ \ subseteq i $在一个字段$ \ mathbb {k} $上响起。我们证明，该模块的初始度在上面是最小发电机的最大程度限制的$ J $。对于图形的边缘理想，给出了Valabrega-Valla模块消失的完整表征。对于更高程度的理想，我们找到了Valabrega-Valla模块消失的类。对于$ j $是混乱$ \ MATHCAL {C} $和$ i $的方面理想的情况，$ j $的单数亚cheme的定义理想是根据$ \ \ natercal {c} $的组合学研究了该模块的不变。最后，我们描述了$ i/j $的REES代数的定义理想，前提是Valabrega-Valla模块为零。
In this paper, we focus on the initial degree and the vanishing of the Valabrega-Valla module of a pair of monomials ideals $J\subseteq I$ in a polynomials ring over a field $\mathbb{K}$. We prove that the initial degree of this module is bounded above by the maximum degree of a minimal generators of $J$. For edge ideals of graphs, a complete characterization of the vanishing of the Valabrega-Valla module is given. For higher degree ideals, we find classes which the Valabrega-Valla module vanishes. For the case that $J$ is the facet ideal of a clutter $\mathcal{C}$ and $I$ is the defining ideal of singular subscheme of $J$, the non-vanishing of this module is investigated in terms of the combinatorics of $\mathcal{C}$. Finally, we describe the defining ideal of the Rees algebra of $I/J$ provided that the Valabrega-Valla module is zero.
