Geodesic
Scattered linear sets generated by collineations between pencils of lines
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 1121-1134.

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Let $A$ and $B$ be two points of $\mathrm{PG}(2,q^n)$, and let $\Phi$ be a collineation between the pencils of lines with vertices $A$ and $B$. In this paper, we prove that the set of points of intersection of corresponding lines under $\Phi$ is either the union of a scattered $\mathrm{GF}(q)$-linear set of rank $n+1$ with the line $AB$ or the union of $q-1$ scattered $\mathrm{GF}(q)$-linear sets of rank $n$ with $A$ and $B$. We also determine the intersection configurations of two scattered $\mathrm{GF}(q)$-linear sets of rank $n+1$ of $\mathrm{PG}(2,q^n)$ both meeting the line $AB$ in a $\mathrm{GF}(q)$-linear set of pseudoregulus type with transversal points $A$ and $B$.
Classification : 51E20, 05B25, 51E21
Keywords: linear sets, collineations, subgeometries 
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     author = {Donati, Giorgio and Durante, Nicola},
     title = {Scattered linear sets generated by collineations between pencils of lines},
     journal = {Journal of Algebraic Combinatorics},
     pages = {1121--1134},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2014__40_4_a1/}
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Donati, Giorgio; Durante, Nicola. Scattered linear sets generated by collineations between pencils of lines. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 1121-1134. http://geodesic.mathdoc.fr/item/JAC_2014__40_4_a1/