Computing minimal Gorenstein covers

Juan Elias (1) , Roser Homs (1) , Bernard Mourrain (2)

1 Departament de Matematiques i Informatica, Universitat de Barcelona
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

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.

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]

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⟩