论文标题
三元张量的特征化学
Eigenschemes of Ternary Tensors
论文作者
论文摘要
我们研究由张量的特征向量（称为征收特征）产生的投射方案。经过一定的一般结果，我们对一般三元对称张量的多种参数特征化进行了异常描述，并计算其尺寸。此外，我们表征了定义三元对称张量的特征cheme的均相多项式三元组的座位。我们的结果使我们能够实现算法来检查给定的一组点是否是对称张量的特征，并重建张量。最后，我们给出了所有还原零维本征的几何表征。我们使用的技术都取决于经典和现代复杂的投影代数几何形状。
We study projective schemes arising from eigenvectors of tensors, called eigenschemes. After some general results, we give a birational description of the variety parametrizing eigenschemes of general ternary symmetric tensors and we compute its dimension. Moreover, we characterize the locus of triples of homogeneous polynomials defining the eigenscheme of a ternary symmetric tensor. Our results allow us to implement algorithms to check whether a given set of points is the eigenscheme of a symmetric tensor, and to reconstruct the tensor. Finally, we give a geometric characterization of all reduced zero-dimensional eigenschemes. The techniques we use rely both on classical and modern complex projective algebraic geometry.
