We introduce and study higher order Jacobian ideals, higher order and mixed Hessians, higher order polar maps, and higher order Milnor algebras associated to a reduced projective hypersurface. We relate these higher order objects to some standard graded Artinian Gorenstein algebras, and we study the corresponding Hilbert functions and Lefschetz properties.

中文翻译：

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高阶Jacobian，Hessian和Milnor代数

我们介绍和研究与减少的投影超曲面有关的高阶Jacobian理想，高阶和混合的Hessian，高阶极坐标图和高阶Milnor代数。我们将这些高阶对象与一些标准等级的Artinian Gorenstein代数相关联，并研究了相应的希尔伯特函数和Lefschetz性质。