On scattered linear sets of pseudoregulus type in PG(1,qt)

• Published in: Finite fields and their applications Vol. 41; pp. 34 - 54
• Main Authors: Csajbók, Bence, Zanella, Corrado
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2016
• Subjects: Finite projective space; Linear set; Normal rational curve; Subgeometry; Finite projective space; Normal rational curve; Subgeometry; 51E20; Linear set
• ISSN: 1071-5797; 1090-2465
• DOI: 10.1016/j.ffa.2016.04.006

Scattered linear sets of pseudoregulus type in PG(1,qt) have been defined and investigated in [19]. The aim of this paper is to continue such an investigation. Properties of a scattered linear set of pseudoregulus type, say L, are proved by means of three different ways to obtain L: (i) as projection of a q-order canonical subgeometry [20], (ii) as a point set whose image under the field reduction map is the hypersurface of degree t in PG(2t−1,q) studied in [10], (iii) as exterior splash, by the correspondence described in [15]. In particular, given a canonical subgeometry Σ of PG(t−1,qt), necessary and sufficient conditions are given for the projection of Σ with center a (t−3)-subspace to be a linear set of pseudoregulus type. Furthermore, the q-order sublines are counted and geometrically described.