Some results on the subadditivity condition of syzygies

Abed Abedelfatah

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arXiv · 2001.01136

Some results on the subadditivity condition of syzygies

Abed Abedelfatah

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Abstract

Among other results, we prove that if $I$ is a monomial ideal of $S=K[x_1,\ldots,x_n]$, where $K$ is a field, and $a\geq b-1\geq0$ are integers such that $a+b\leq\mathrm{proj~dim}(S/I)$, then $$t_{a+b}\leq t_a+t_1+t_2+\cdots+t_b-\frac{b(b-1)}{2},$$ where $t_1,t_2,\dots$ are the maximal shifts in the minimal graded free $S$-resolution of $S/I$.

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Abed Abedelfatah. 2020-01-04. Some results on the subadditivity condition of syzygies. https://arxiv.org/abs/2001.01136

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