Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs

Abstract

Let $G$ be a bipartite graph and $I=I(G)$ be its edge ideal. The aim of this note is to investigate different aspects of the Rees algebra $\mathcal{R}(I)$ of $I$. We compute its regularity and the universal Gröbner basis of its defining equations; interestingly, both of them are described in terms of the combinatorics of $G$. We apply these ideas to study the regularity of the powers of $I$. For any $s\ge \text{match}(G)+|E(G)|+1$ we prove that $\text{reg}(I^{s+1})=\text{reg}(I^s)+2$.

to appear in Le Matematiche

References in corpus (1)

• Homological properties of bigraded algebras