An iterative construction of Gorenstein ideals

In this paper, we present a method to inductively construct Gorenstein ideals of any codimension We start from a Gorenstein ideal of codimension contained in a complete intersection ideal of the same codimension, and we prove that under suitable hypotheses there exists a new Gorenstein ideal contained in the residual ideal We compare some numerical data of the starting and the resulting Gorenstein ideals of the construction. We compare also the Buchsbaum-Eisenbud matrices of the two ideals, in the codimension three case. Furthermore, we show that this construction is independent from the other known geometrical constructions of Gorenstein ideals, providing examples.