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Section: New Results

Computing minimal Gorenstein covers

Participant : Bernard Mourrain.

In [7], 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]]/I such that (G)-(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.

This is a joint work with Juan Elias and Roser Homs (Dep. de Matematiques i Informatica, Universitat de Barcelona).