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arXiv · 2207.02256

Arithmetical rank and cohomological dimension of generalized binomial edge ideals

Anargyros Katsabekis
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Abstract

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.

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Anargyros Katsabekis. 2022-07-05. Arithmetical rank and cohomological dimension of generalized binomial edge ideals. https://arxiv.org/abs/2207.02256

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