Mapping free resolutions of length three II - Module formats

Let M be a perfect module of projective dimension 3 over a Gorenstein, local or graded ring R. We denote by F the minimal free resolution of M. Using the generic ring associated to the format of F we define higher structure maps, according to the theory developed by Weyman in [26]. We introduce a generalization of classical linkage for R-module using the Buchsbaum–Rim complex, and study the behavior of structure maps under this Buchsbaum–Rim linkage. In particular, for certain formats we obtain criteria for these R-modules to lie in the Buchsbaum–Rim linkage class of a Buchsbaum–Rim complex of length 3.