Let A be a noetherian local
ring, and let C in ℙA3 be a family of curves, flat over A. We showed in an earlier
paper how to associate to C a locally free sheaf N on ℙA3, 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′ are pseudo-isomorphic (generalization of the theorem Rao). In this
paper we show how to find all the flat families of curves C associated to a given
locally free sheaf N and its twists, starting with the minimal family C0. We show also
that all other families are obtained from the minimal family by a sequence of
elementary biliaisons and a deformation (generalization of the theorem of
Lazarsfeld Rao). The calculations are algorithmic in terms of a presentation of
N.
