Computing Minimal Gorenstein Covers

We analyze and present an effective solution to the minimal Gorenstein cover problem: given a local Artin k-algebra A=k〚x1,…,xn〛/I, compute an Artin Gorenstein k-algebra G=k〚x1,…,xn〛/J such that ℓ(G)−ℓ(A) is minimal. We approach the problem by using Macaulay's inverse systems and a modification of the integration method for inverse systems to compute Gorenstein covers. We propose new characterizations of the minimal Gorenstein cover and present a new algorithm for the effective computation of the variety of all minimal Gorenstein covers of A for low Gorenstein colength. Experimentation illustrates the practical behavior of the method.