Generalized k-configurations and their minimal free resolutions

In this paper, we find the minimal free resolution of each weak kD-configuration, a generalization of k-configurations which we introduced in (Generalized k-configurations, Canad. J. Math., February 2003, submitted for publication). We then apply this result to show that, like k-configurations, weak kD-configurations satisfy the property that every socle-permissible value actually occurs as the degree of some point. Furthermore, we describe a sense in which weak kD-configurations have an extremal resolution. Finally, our methods allow us to find an infinite class of Hilbert functions for which no unique smallest minimal free resolution is possible for that Hilbert function. (See J. Algebra 244 (2001) 236 for other such classes.).