论文标题
警告和仙人掌等级以及对称形式的an灭者的强大属性
Waring and cactus ranks and Strong Lefschetz Property for annihilators of symmetric forms
论文作者
论文摘要
在本说明中，我们表明，完整的对称多项式是压缩的Artinian Gorenstein代数的双重发电机，满足了强Lefschetz属性。这是具有这些属性的显式二元形式的第一个示例。 对于任何数量变量的任何程度的完整对称形式，我们通过建立明确的功率总和分解来为警告等级提供上限。 此外，我们确定了由对称立方形式定义的任何Gorenstein代数的Waring等级，仙人掌等级，仙人掌等级，分辨率和强烈的Lefschetz特性。特别是，我们表明，可以通过增加变量的数量来任意使对称立方形式的Waring等级与仙人掌等级之间的差异任意大大。 我们为四个和五个学位的通用对称形式的警告等级提供上限。
In this note we show that the complete symmetric polynomials are dual generators of compressed artinian Gorenstein algebras satisfying the Strong Lefschetz Property. This is the first example of an explicit dual form with these properties. For complete symmetric forms of any degree in any number of variables, we provide an upper bound for the Waring rank by establishing an explicit power sum decomposition. Moreover, we determine the Waring rank, the cactus rank, the resolution and the Strong Lefschetz Property for any Gorenstein algebra defined by a symmetric cubic form. In particular, we show that the difference between the Waring rank and the cactus rank of a symmetric cubic form can be made arbitrarily large by increasing the number of variables. We provide upper bounds for the Waring rank of generic symmetric forms of degrees four and five.
