A note on the subadditivity of Syzygies

Sabine El Khoury, Hema Srinivasan

Published 2016-02-05Version 1

Let $R=S/I$ be a graded algebra with $t_i$ and $T_i$ being the minimal and maximal shifts in the minimal $S$ resolution of $R$ at degree $i$. In this paper we prove that $t_n\leq t_1+T_{n-1}$, for all $n$ and as a consequence, we show that for Gorenstein algebras of codimension $h$, the subadditivity of maximal shifts $T_i$ in the minimal resolution holds for $i \le h-1$, i.e, we show that $T_i \leq T_a+T_{i-a}$ for $i\le h-1$.