论文标题
Cubic四倍和其他Artinian代数的Jacobian环的Lefschetz属性
Lefschetz properties for jacobian rings of cubic fourfolds and other Artinian algebras
论文作者
论文摘要
在本文中，我们利用了一些几何分化技术来证明具有$ 1 $ $ 1 $的强Lefschetz属性，用于完整的相交标准标准的Artinian Gorenstein代数Codimension $ 6 $由Quadrics提出。我们还证明了在较高的编成中，同样类型的Artinian代数具有一些强的Lefschetz特性。此外，我们分析了一些自然而然地融入“特殊” Artinian代数的基因座：对他们来说，我们提供了一些几何描述，并在所谓的非lefschetz基因座的非空虚中以$ 1 $ 1 $的价格与弱小的Lefschetz属性的“提升”的“提升”的“ lefs”。
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.
