论文标题
广义二项式边缘理想的算术等级和共同体学维度
Arithmetical rank and cohomological dimension of generalized binomial edge ideals
论文作者
论文摘要
令$ g $为顶点集$ [n] $上的连接且简单的图。对于图$ g $，一个人可以在多项式环$ r = k [x_ {ij}：i \ in [m]，j \ in [n] $中关联一般的二项式边缘理想$ j_ {m}（g）$。我们为$ j_ {m}（g）$的共同体学维度提供了下限。我们还研究$ j_ {m}（g）$是一个共同的交叉点。最后，我们证明$ j_ {2}（g）$的算术等级等于$ r/j_ {2}（g）$在几种情况下的投影尺寸。
Let $G$ be a connected and simple graph on the vertex set $[n]$. To the graph $G$ one can associate the generalized binomial edge ideal $J_{m}(G)$ in the polynomial ring $R=K[x_{ij}: i \in [m], j \in [n]]$. We provide a lower bound for the cohomological dimension of $J_{m}(G)$. We also study when $J_{m}(G)$ is a cohomologically complete intersection. Finally, we show that the arithmetical rank of $J_{2}(G)$ equals the projective dimension of $R/J_{2}(G)$ in several cases.
