Subgeometries in the André/Bruck-Bose representation

2014/09/22 by Sara Rottey, Rottey, Sara, John Sheekey +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1409.6123

arxiv created 2014/09/22 · arxiv updated 2014/09/23

Abstract

We consider the André/Bruck-Bose representation of the projective plane PG(2,qⁿ) in PG(2n,q). We investigate the representation of \mathbbF_q^k-sublines and \mathbbF_q^k-subplanes of PG(2,qⁿ), extending the results for n=3 of \citeBarJack2 and correcting the general result of \citeBarJack1. We characterise the representation of \mathbbF_q^k-sublines tangent to or contained in the line at infinity, \mathbbF_q-sublines external to the line at infinity, \mathbbF_q-subplanes tangent to and \mathbbF_q^k-subplanes secant to the line at infinity.

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