Construction of minimal families of space curves

Let A be a noetherian local ring, and let C in P-A(3) be a family of curves , at over A. We showed in an earlier paper how to associate to C a locally free sheaf N on P-A(2), and we showed that two families of curves C,C' are in the same biliaison class if and only if the corresponding sheaves N,N' a re pseudoisomorphic (generalization of the theorem Rao). In this paper we s how how to find all the at families of curves C associated to a given local ly free sheaf N and its twists, starting with the minimal family C-0. We sh ow also that all other families are obtained from the minimal family by a s equence of elementary biliaisons and a deformation (generalization of the t heorem of Lazarsfeld Rao). The calculations are algorithmic in terms of a p resentation of N.