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Computing minimal Gorenstein covers

Juan Elias 1 Roser Homs 1 Bernard Mourrain 2
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA | UoA - National and Kapodistrian University of Athens = University of Athens
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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Submitted on : Monday, October 28, 2019 - 12:03:15 PM
Last modification on : Tuesday, January 14, 2020 - 1:36:09 PM

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

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