Generalized \(k\)-configurations and their minimal free resolutions
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.
scientific article; zbMATH DE number 2093445