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arXiv · 1602.02116

A note on the subadditivity of Syzygies

Sabine El Khoury·Hema Srinivasan
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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 $i\geq h-1$.

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Sabine El Khoury, Hema Srinivasan. 2016-02-05. A note on the subadditivity of Syzygies. https://arxiv.org/abs/1602.02116

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