Arithmetical rank and cohomological dimension of generalized binomial edge ideals

Abstract

Let [Formula: see text] be a connected and simple graph on the vertex set [Formula: see text]. To the graph [Formula: see text] one can associate the generalized binomial edge ideal [Formula: see text] in the polynomial ring [Formula: see text]. We provide a lower bound for the cohomological dimension of [Formula: see text]. We also study when [Formula: see text] is a cohomologically complete intersection. Finally, we show that the arithmetical rank of [Formula: see text] equals the projective dimension of [Formula: see text] in several cases.