Every linear set in a projective 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 h-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 h-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 h-scattered linear sets of h-pseudoregulus type.

Linear sets from projection of Desarguesian spreads / Napolitano, V.; Polverino, O.; Zini, G.; Zullo, F.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 71:(2021), pp. 1-19. [10.1016/j.ffa.2020.101798]

Linear sets from projection of Desarguesian spreads

Zini G.;
2021

Abstract

Every linear set in a projective 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 h-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 h-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 h-scattered linear sets of h-pseudoregulus type.
2021
71
1
19
Linear sets from projection of Desarguesian spreads / Napolitano, V.; Polverino, O.; Zini, G.; Zullo, F.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 71:(2021), pp. 1-19. [10.1016/j.ffa.2020.101798]
Napolitano, V.; Polverino, O.; Zini, G.; Zullo, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1258221
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