论文标题
$ a $ fold产品产生的线性形式产生的理想具有线性分级的免费分辨率
Ideals generated by $a$-fold products of linear forms have linear graded free resolution
论文作者
论文摘要
给定$σ\ subset r：= \ mathbb k [x_1，\ ldots，x_k] $，其中$ \ mathbb k $是一个特征性0的领域，任何有限的线性形式集合，有些可能是比例的，以及任何$ 1 \ leq a \ leq a \ leq a \ leq a \ leq |σ| $ f ud $ i $ i _A（$ i__a（$ i__a $ i _），$ i_a（$ i_a n $ fifice a $ i _A（$ i_）（$ i _A（$ i _）（$ i_a）（$ i_A（$ i_）， $σ$，具有线性分级的免费分辨率。这使我们能够确定一个生成集，以定义理想的定义理想的Orlik-terao代数的第二顺序排列中的$ \ Mathbb p _ {\ Mathbb {k}}^2 $，并得出结论，以$ k = 3 $和$σ$定义了$ q uipr的$ k = 3 $，并定义了$ quirl的$ quirl，$ IS $ IS $ IS $ ies = _____________c.我们还证明了几种符号力量的猜想，用于定义任何编码$ c $的星形配置理想。
Given $Σ\subset R:=\mathbb K[x_1,\ldots,x_k]$, where $\mathbb K$ is a field of characteristic 0, any finite collection of linear forms, some possibly proportional, and any $1\leq a\leq |Σ|$, we prove that $I_a(Σ)$, the ideal generated by all $a$-fold products of $Σ$, has linear graded free resolution. This allows us to determine a generating set for the defining ideal of the Orlik-Terao algebra of the second order of a line arrangement in $\mathbb P_{\mathbb{K}}^2$, and to conclude that for the case $k=3$, and $Σ$ defining such a line arrangement, the ideal $I_{|Σ|-2}(Σ)$ is of fiber type. We also prove several conjectures of symbolic powers for defining ideals of star configurations of any codimension $c$.
