In this paper we contribute towards the classification of partially symmetric tensors in \({\mathbb {F}}_q^3\otimes S^2{\mathbb {F}}_q^3\), q even, by classifying planes which intersect the Veronese surface \({\mathcal {V}}({\mathbb {F}}_q)\) in at least one point, under the action of \(K\le \textrm{PGL}(6,q)\), \(K\cong \textrm{PGL}(3,q)\), stabilising the Veronese surface. We also determine a complete set of geometric and combinatorial invariants for each of the orbits.

中文翻译：

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在偶数阶有限域上与 Veronese 曲面相交的平面分类

在本文中，我们对 \({\mathbb {F}}_q^3\otimes S^2{\mathbb {F}}_q^3\) 中的部分对称张量的分类做出了贡献，甚至通过对平面进行分类与 Veronese 曲面\({\mathcal {V}}({\mathbb {F}}_q)\)相交至少一点，在\(K\le \textrm{PGL}(6,q)的作用下\) , \(K\cong \textrm{PGL}(3,q)\)，稳定 Veronese 表面。我们还为每个轨道确定了一组完整的几何和组合不变量。