A note on the subadditivity of Syzygies

Sabine El Khoury; Hema Srinivasan

paper

A note on the subadditivity of Syzygies

arXiv:1602.02116

Abstract

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 $i \geq h - 1$ , i.e, we show that $T_{i} \leq T_{a} + T_{i - a}$ for $i \geq h - 1$ .

arXiv comment4 pages