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arXiv · 1901.04165

Computing minimal Gorenstein covers

Juan Elias·Roser Homs·Bernard Mourrain
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Abstract

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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Juan Elias, Roser Homs, Bernard Mourrain. 2019-01-14. Computing minimal Gorenstein covers. https://arxiv.org/abs/1901.04165

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