Scattered linear sets of pseudoregulus type in PG(1,q^t) have been defined and investigated in [19, 5]. 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 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,q^t), 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.
On scattered linear sets of pseudoregulus type in PG(1,q^t)
CSAJBOK, BENCE;ZANELLA, CORRADO
2016
Abstract
Scattered linear sets of pseudoregulus type in PG(1,q^t) have been defined and investigated in [19, 5]. 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 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,q^t), 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.
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