Scattered linear sets and pseudoreguli (Q1953394)

Summary: In this paper, we show that one can associate a pseudoregulus with every scattered linear set of rank \(3n\) in \(\mathrm{PG}(2n-1,q^3)\). We construct a scattered linear set having a given pseudoregulus as associated pseudoregulus and prove that there are \(q-1\) different scattered linear sets that have the same associated pseudoregulus. Finally, we give a characterisation of reguli and pseudoreguli in \(\mathrm{PG}(3,q^3)\).