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Journal Articles Journal of Pure and Applied Algebra Year : 2019

Computing minimal Gorenstein covers


We analyze and present an effective solution to the minimal Gorenstein cover problem: given a local Artin k-algebra $A = k[[x 1 ,. .. x n ]]/I$, compute an Artin Gorenstein $k$-algebra $G = k[[x 1 ,. .. x n ]]/J$ such that $\ell(G)−\ell(A)$ 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.
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Dates and versions

hal-01978906 , version 1 (11-01-2019)
hal-01978906 , version 2 (28-10-2019)



Juan Elias, Roser Homs, Bernard Mourrain. Computing minimal Gorenstein covers. Journal of Pure and Applied Algebra, 2019, ⟨10.1016/j.jpaa.2019.106280⟩. ⟨hal-01978906v2⟩
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