论文标题
$ a_i $ -invariants的理想力量
$a_i$-invariants of powers of ideals
论文作者
论文摘要
受Lu和O'Rourke最近的工作的启发，我们研究了某些分级理想的$ A_I $ invariants（符号）力量。第一种情况是当$ i $和$ j $是两个不同的多项式环$ r $和$ s $上的两个分级理想时，$ \ mathbb {k} $。我们通过$ i $和$ j $的相应知识来研究光纤产品幂的$ a_i $ invariants。第二种情况是$i_Δ$是$ k $二维的简单复合物$δ$，带有$ k \ ge 2 $的理想。我们研究了$i_Δ$的符号功率的$ a_i $ invariants。
Inspired by the recent work of Lu and O'Rourke, we study the $a_i$-invariants of (symbolic) powers of some graded ideals. The first scenario is when $I$ and $J$ are two graded ideals in two distinct polynomial rings $R$ and $S$ over a common field $\mathbb{K}$. We study the $a_i$-invariants of the powers of the fiber product via the corresponding knowledge of $I$ and $J$. The second scenario is when $I_Δ$ is the Stanley-Reisner ideal of a $k$-dimensional simplicial complex $Δ$ with $k\ge 2$. We investigate the $a_i$-invariants of the symbolic powers of $I_Δ$.
