论文标题
警告问题和lefschetz属性
Waring problems and the Lefschetz properties
论文作者
论文摘要
我们研究了多项式的警告问题的三种变体，涉及形式的尾巴等级，边界等级和仙人掌等级，我们展示了相关代数的lefschetz属性如何影响它们。主要工具是混合黑森州矩阵的理论。我们构建了野生形式的新家庭，即，其仙人掌等级（示意性本质）比边界等级更大的形式。
We study three variations of the Waring problem for polynomials, concerning the Waring rank, the border rank and the cactus rank of a form and we show how the Lefschetz properties of the associated algebra affect them. The main tool is the theory of mixed Hessian matrix. We construct new families of wild forms, that is, forms whose cactus rank, of schematic nature, is bigger then the border rank, defined geometrically.
