In this paper, we exploit some geometric-differential techniques to prove the strong Lefschetz property in degree 1 for a complete intersection standard Artinian Gorenstein algebra of codimension 6 presented by quadrics. We prove also some strong Lefschetz properties for the same kind of Artinian algebras in higher codimensions. Moreover, we analyze some loci that come naturally into the picture of “special” Artinian algebras: for them we give some geometric descriptions and show a connection between the non emptiness of the so-called non-Lefschetz locus in degree 1 and the “lifting” of a weak Lefschetz property to an algebra from one of its quotients.

在本文中，我们利用一些几何微分技术来证明由二次曲面表示的余维 6 的完全交集标准 Artinian Gorenstein 代数在 1 阶中的强 Lefschetz 性质。我们还证明了相同类型的高余维 Artinian 代数的一些强 Lefschetz 性质。此外，我们分析了一些自然出现在“特殊”Artinian 代数图片中的轨迹：我们对它们进行了一些几何描述，并展示了所谓的 1 级非 Lefschetz 轨迹的非空性与“提升”之间的联系” 弱 Lefschetz 属性从其商之一到代数。