论文标题
加权图表中的符号功率
Symbolic powers in weighted oriented graphs
论文作者
论文摘要
当非平凡权重的顶点是水槽和$ i（d）时，让$ d $是带有基础图$ g $的加权图形图，i（g）$分别是对应于$ d $ g和$ g的边缘理想。我们使用强顶点封面的概念对$ i（d）$的符号功能进行明确描述。我们表明，$ i（d）$和$ i（g）$的普通和象征性权力以类似的方式行事。我们为某些类别的加权图形图提供了符号功率的描述和$ i（d）$的waldschmidt常数。当$ d $是一个加权的奇数周期时，我们计算$ \ reg（i（d）^{（s）}/i（d）^s）$，并证明$ \ reg I（d）^{（s）} \ leq \ reg iq \ reg i（d）^s $，并显示出一个仅具有非trivial量的vertex时，则表现出了平等。
Let $D$ be a weighted oriented graph with the underlying graph $G$ when vertices with non-trivial weights are sinks and $I(D), I(G) $ be the edge ideals corresponding to $D$ and $G,$ respectively. We give explicit description of the symbolic powers of $I(D)$ using the concept of strong vertex covers. We show that the ordinary and symbolic powers of $I(D)$ and $I(G)$ behave in a similar way. We provide a description for symbolic powers and Waldschmidt constant of $I(D)$ for certain classes of weighted oriented graphs. When $D$ is a weighted oriented odd cycle we compute $\reg (I(D)^{(s)}/I(D)^s)$ and prove $\reg I(D)^{(s)}\leq\reg I(D)^s$ and show that equality holds when there is only one vertex with non-trivial weight.
