论文标题
某些编码三个Artinian Gorenstein代数的Lefschetz特性
Lefschetz properties of some codimension three Artinian Gorenstein algebras
论文作者
论文摘要
编成两个Artinian代数$ A $具有强大和弱的Lefschetz属性，前提是特征比Socle学位更大或大。这种结果在多大程度上可能扩展到三个AG代数 - 到目前为止，最有希望的结果涉及此类代数的Lefschetz属性。我们在这里表明，每个标准级别的编码三个Artinian Gorenstein代数$ a $具有Hilbert函数最大值的最大值（最多六）具有强大的Lefschetz属性，前提是该特征为零。当特征大于$ a $的Socle学位时，我们表明$ a $几乎是强大的lefschetz。然而，这种相当谦虚的结果可以说是到目前为止最包含的，它是针对分级的codimension三个AG代数的强Lefschetz属性。
Codimension two Artinian algebras $A$ have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras - the most promising results so far have concerned the weak Lefschetz property for such algebras. We here show that every standard-graded codimension three Artinian Gorenstein algebra $A$ having low maximum value of the Hilbert function - at most six - has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of $A$, we show that $A$ is almost strong Lefschetz. This quite modest result is nevertheless arguably the most encompassing so far concerning the strong Lefschetz property for graded codimension three AG algebras.
