Acyclicity criteria for complexes associated with an alternating map

Tchernev, Alexandre

doi:10.1090/S0002-9939-01-05935-4

Acyclicity criteria for complexes associated with an alternating map
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by Alexandre B. Tchernev PDF

Proc. Amer. Math. Soc. 129 (2001), 2861-2869 Request permission

Abstract:

When $I$ is a Gorenstein ideal of grade $3$ in a local ring $R$, results of Boffi and Sánchez, and of Kustin and Ulrich show that for each $t\ge 1$ one can construct in a canonical way a finite free complex $\mathcal {D}^{t}$ that is “approximately" a resolution for the ideal $I^{t}$. Kustin and Ulrich also provide a sufficient condition that $\mathcal {D}^{t}$ is acyclic, and a sufficient condition that $\mathcal {D}^{t}$ is a resolution of $I^{t}$. We complete these two acyclicity criteria by showing that the corresponding sufficient conditions are also necessary.

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