A note on the subadditivity of Syzygies

作者：El Khoury Sabine^*; Srinivasan Hema

来源：Journal of Algebra and Its Applications, 2017, 16(9): 1750177.

DOI：10.1142/S0219498817501778

• Graded resolutions
• Gorenstein algebras

Let R = S/I be a graded algebra with t(i) and T-i being the minimal and maximal shifts in the minimal graded free resolution of R at degree i. We prove that t(n) <= t(1) + Tn-1 for all n. As a consequence, we show that for Gorenstein algebras of codimension h, the subadditivity of maximal shifts T-n in the minimal graded free resolution holds for n >= h - 1, i.e. we show that T-n = T-a + Tn-a for n >= h - 1.

• 出版日期2017-9