Equations of the multi-Rees algebra of fattened coordinate subspaces

Abstract

In this paper, we describe the equations defining the multi-Rees algebra [Formula: see text] ([Formula: see text]), where the ideals are generated by subsets of [Formula: see text]. We also show that a family of binomials whose leading terms are squarefree, form a Gröbner basis for the defining equations with lexicographic order. We show that if we remove binomials that include [Formula: see text]’s, then remaining binomials form a Gröbner basis for the toric ideal associated to the multi-fiber ring. However binomials, including [Formula: see text]’s, in Gröbner basis of defining equations of the multi-Rees algebra are not necessarily defining equations of corresponding symmetric algebra. Despite this fact, we show that this family of ideals is of multi-fiber type.