On subspaces defining linear sets of maximum rank

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Abstract

Let V denote an r-dimensional Fₐ䂞-vector space. Let U and W be Fq-subspaces of V, LU and LW the projective points of PG\, (V, qⁿ) defined by U and W respectively. We address the problem when LW=LU under the hypothesis that U and W have maximum dimension, i. e. , ₅ₐ W=₅ₐU= rn-n, and we give a complete characterization for r=2.

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Valentina Pepe (Sun,) studied this question.

synapsesocial.com/papers/68e75efdb6db6435876d60d0 https://doi.org/https://doi.org/10.48550/arxiv.2403.01551

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