由Desklesian价差投影得到的线性集
Linear sets from projection of Desarguesian spreads
摘要：
伽罗瓦空间中的每个线性集都是一个子几何的投影，大多数已知的线性集的刻画都是在这个观点下给出的。例如，伪正则型的散布线性集是通过考虑子几何的一个Desklesian展开，并从一个顶点投影得到的，该顶点被除了两个指向矢空间之外的所有指向矢空间所张成。本文引入了$h$ -pseudoregulus型线性集的概念，证明了它是从一个子几何的Despermesian展开的任意数目的指向矢空间的跨距上投影出来的。在这些线性集，我们的特点是$h$ -分散和解决它们之间的等价性问题，最近在文献中介绍的代数工具，被称为摩尔指数集发挥了关键作用。作为一个副产品，我们分类渐近$h$ -分散线性集的$h$ -pseudoregulus类型。
英文摘要：
Every linear set in a Galois space is the projection of a subgeometry, and most known characterizations of linear sets are given under this point of view. For instance, scattered linear sets of pseudoregulus type are obtained by considering a Desarguesian spread of a subgeometry and projecting from a vertex which is spanned by all but two director spaces. In this paper we introduce the concept of linear sets of $h$-pseudoregulus type, which turns out to be projected from the span of an arbitrary number of director spaces of a Desarguesian spread of a subgeometry. Among these linear sets, we characterize those which are $h$-scattered and solve the equivalence problem between them; a key role is played by an algebraic tool recently introduced in the literature and known as Moore exponent set. As a byproduct, we classify asymptotically $h$-scattered linear sets of $h$-pseudoregulus type.
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