A note on the subadditivity of Syzygies

Abstract

Let R = S/I be a graded algebra with ti and Ti being the minimal and maximal shifts in the minimal graded free resolution of R at degree i. We prove that tn ≤ t1 + Tn-1 for all n. As a consequence, we show that for Gorenstein algebras of codimension h, the subadditivity of maximal shifts Tn in the minimal graded free resolution holds for n ≥ h-1, i.e. we show that Tn ≤ Ta + Tn-A for n ≥ h-1. © 2017 World Scientific Publishing Company.