Maria Evelina Rossi: A constructive approach to d-dimensional Gorenstein k-algebras

Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras.  To date a general  structure for  Gorenstein rings  of any dimension (and codimension) is not understood. We extend Macaulay's correspondence  characterizing  the submodules of the polynomial ring in one-to-one correspondence with Gorenstein d-dimensional k-algebras.  We discuss effective methods for constructing Gorenstein graded rings of given multiplicity and regularity. Several examples illustrating the results are given.