# Computing minimal Gorenstein covers

2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , National and Kapodistrian 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.
Document type :
Preprints, Working Papers, ...

https://hal.inria.fr/hal-01978906
Contributor : Bernard Mourrain <>
Submitted on : Friday, January 11, 2019 - 8:52:54 PM
Last modification on : Monday, January 21, 2019 - 2:54:01 PM

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### Identifiers

• HAL Id : hal-01978906, version 1
• ARXIV : 1901.04165

### Citation

Juan Elias, Roser Homs, Bernard Mourrain. Computing minimal Gorenstein covers. 2019. 〈hal-01978906〉

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