Gorenstein Points In P³

After the structure theorem of Buchsbaum and Eisenbud [1] on Gorenstein ideals of codimension 3, much progress was made in this area from the algebraic point of view; in particular some characterizations of these ideals using h−vectors (Stanley [9]) and minimal resolutions (Diesel [3]) were given. On the other hand, the Liaison theory gives some tools to exploit, but, at the same time, it requires one to find, from the geometric point of view, new Gorenstein schemes. The works of Geramita-Migliore [5] and Migliore-Nagel [6] present some constructions for Gorenstein schemes of codimension 3; in particular they deal with points in P3. Starting from the work of Migliore and Nagel, we study their constructions and we give a new construction for points in P3: given a specific subset of a plane complete intersection, we add a “suitable” set of points on a line not in the plane and we obtain an aG zeroscheme that is not complete intersection. We emphasize the interesting fact that, by this method, we are able to “visualize” where these points live.