Arithmetical rank and cohomological dimension of generalized binomial edge ideals

Anargyros Katsabekis

paper

Arithmetical rank and cohomological dimension of generalized binomial edge ideals

arXiv:2207.02256

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.

Journal of Algebra and its Applications (to appear)