Abstract In this paper we investigate the geometric properties of the configuration consisting of a subspace Γ and a canonical subgeometry Σ in PG ( n − 1 , q n ) , with Γ ∩ Σ = 0 . The idea motivating is that such properties are reflected in the algebraic structure of the linear set which is projection of Σ from the vertex Γ . In particular we deal with the maximum scattered linear sets of the line PG ( 1 , q n ) found by Lunardon and Polverino (2001) and recently generalized by Sheekey (2016). Our aim is to characterize this family by means of the properties of the vertex of the projection as done by Csajbok and the first author of this paper for linear sets of pseudoregulus type. With reference to such properties, we construct new examples of scattered linear sets in PG ( 1 , q 6 ) , yielding also to new examples of MRD-codes in F q 6 × 6 with left idealizer isomorphic to F q 6 .

中文翻译：

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PG(1,qn) 的最大分散线性集的顶点属性

摘要 在本文中，我们研究了PG (n − 1, qn ) 中由子空间Γ 和规范子几何Σ 组成的构型的几何性质，其中Γ ∩ Σ = 0 。激励的想法是这些属性反映在线性集的代数结构中，线性集是 Σ 从顶点 Γ 的投影。特别是我们处理由 Lunardon 和 Polverino (2001) 发现并最近由 Sheekey (2016) 概括的线 PG ( 1 , qn ) 的最大分散线性集。我们的目标是通过投影顶点的属性来表征这个家族，正如 Csajbok 和本文的第一作者对伪正则类型的线性集所做的那样。参考这些性质，我们在 PG ( 1 , q 6 ) 中构造新的分散线性集的例子，