论文标题
长度3和连锁的免费分辨率的较高结构地图
Higher structure maps for free resolutions of length 3 and linkage
论文作者
论文摘要
让$ i $是Gorenstein Local Ring $ r $的高度3的理想理想。令$ \ mathbb {f} $为$ i $的最低免费分辨率。可以使用与$ \ Mathbb {f} $的格式关联的通用环来定义的一系列线性图，该序列可以概括$ \ mathbb {f} $的乘法结构。让$ j $是与$ i $相关的理想选择。我们提供公式，以根据$ i $的免费分辨率来计算$ j $的免费分辨率。我们将结果应用于描述LICCI理想的类别，表明当Betti数字$（1,5,6,2）$的完美理想是LICCI时，并且仅当这些地图中至少是nonzero modulo中的最大理想是$ r $的最大理想。
Let $I$ be a perfect ideal of height 3 in a Gorenstein local ring $R$. Let $\mathbb{F}$ be the minimal free resolution of $I$. A sequence of linear maps, which generalize the multiplicative structure of $\mathbb{F}$, can be defined using the generic ring associated to the format of $\mathbb{F}$. Let $J$ be an ideal linked to $I$. We provide formulas to compute some of these maps for the free resolution of $J$ in terms of those of the free resolution of $I$. We apply our results to describe classes of licci ideals, showing that a perfect ideal with Betti numbers $(1,5,6,2)$ is licci if and only if at least one of these maps is nonzero modulo the maximal ideal of $R$.
