Let $I$ be a monomial ideal in two variables generated by three monomials and let $\mathcal{ R}(I)$ be its Rees ideal. We describe an algorithm to compute the minimal generating set of $\mathcal{ R}(I)$. Based on the data obtained by this algorithm, we build a graph that encodes the minimal free resolution of $\mathcal{ R}(I)$. We explicitly describe the modules and differentials on the minimal free resolution of $\mathcal{ R}(I)$.
Categories: math.AC math.AG math.RA