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 behaviour 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.