Arithmetical rank of strings and cycles

Abstract

Let $R$ be a polynomial ring over a field~$K$. To a given squarefree monomial ideal $I \subset R$, one can associate a hypergraph $\mathcal{H} (I)$. In this article, we prove that the arithmetical rank of $I$ is equal to the projective dimension of $R/I$ when $\mathcal{H} (I)$ is a string or a cycle hypergraph.