Generalized \(k\)-configurations and their minimal free resolutions (Q1878442)

Let \(k\) be an algebraically closed field of characterisitc zero, \(D=\{d_1,\dots,d_r\}\) a set of positive integers. The notion of \(k_D\)-configuration was introduced by the author [Can. J. Math. 57, No.2, 400--415 (2005; Zbl 1083.14055)] generalizing the notion of \(k\)-configuration introduced by \textit{A. V. Geramita, P. Maroscia} and \textit{L. G. Roberts} [J. Lond. Math. Soc. 28, 443--452 (1983; Zbl 0535.13012)]. Here the author finds the minimal free resolution of each weak \(k_D\)-configuration. Several applications are given. For example, the author finds an infinite class of Hilbert functions for which no unique smallest minimal free resolution can exist for that Hilbert function.