Linear sets from projection of Desarguesian spreads
Abstract
Every linear set in a Galois space is the projection of a subgeometry, and most known characterizations of linear sets are given under this point of view. For instance, scattered linear sets of pseudoregulus type are obtained by considering a Desarguesian spread of a subgeometry and projecting from a vertex which is spanned by all but two director spaces. In this paper we introduce the concept of linear sets of -pseudoregulus type, which turns out to be projected from the span of an arbitrary number of director spaces of a Desarguesian spread of a subgeometry. Among these linear sets, we characterize those which are -scattered and solve the equivalence problem between them; a key role is played by an algebraic tool recently introduced in the literature and known as Moore exponent set. As a byproduct, we classify asymptotically -scattered linear sets of -pseudoregulus type.
Cite
@article{arxiv.2001.08685,
title = {Linear sets from projection of Desarguesian spreads},
author = {Vito Napolitano and Olga Polverino and Giovanni Zini and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2001.08685},
year = {2020}
}