论文标题
在有限字段上警告可识别的子空间
Waring identifiable subspaces over finite fields
论文作者
论文摘要
Waring的问题是将整数表达为权力之和，历史悠久，可以追溯到17世纪，并且在许多不同的情况下已经研究了问题。在本文中，我们介绍了有关射影的代数品种$ \ Mathcal X $的警告子空间和可识别的子空间的概念。当$ \ Mathcal X $是Veronese品种时，这些子空间在对称张量理论中起着基本作用，并且与对称张量（均匀的多项式）的战争分解和识别性识别性有关。我们在$ {\ MathBb {p}}}^5（{\ Mathbb {f}} _ q）$中给出了有关Veronese品种的几个构造和分类结果，以$ {\ MathBb {p}}}^5（{\ Mathbb {f}} _ Q）$和$ {\ Mathbb {p}}}}^9}^{9}（\ Mathbb} $ { $ {\ mathbb {p}}}^3（{\ mathbb {f}} _ q）$中的四边形的线性系统。
Waring's problem, of expressing an integer as the sum of powers, has a very long history going back to the 17th century, and the problem has been studied in many different contexts. In this paper we introduce the notion of a Waring subspace and a Waring identifiable subspace with respect to a projective algebraic variety $\mathcal X$. When $\mathcal X$ is the Veronese variety, these subspaces play a fundamental role in the theory of symmetric tensors and are related to the Waring decomposition and Waring identifiability of symmetric tensors (homogeneous polynomials). We give several constructions and classification results of Waring identifiable subspaces with respect to the Veronese variety in ${\mathbb{P}}^5({\mathbb{F}}_q)$ and in ${\mathbb{P}}^{9}({\mathbb{F}}_q)$, and include some applications to the theory of linear systems of quadrics in ${\mathbb{P}}^3({\mathbb{F}}_q)$.
