Non-classical hyperplanes of finite thick dual polar spaces
The electronic journal of combinatorics, Tome 25 (2018) no. 1
We obtain a classification of the nonclassical hyperplanes of all finite thick dual polar spaces of rank at least 3 under the assumption that there are no ovoidal and semi-singular hex intersections. In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive. As a corollary, we also obtain a classification of the nonclassical hyperplanes of $DW(2n-1,q)$, $q$ even. In particular, we obtain a complete classification of all nonclassical hyperplanes of $DW(2n-1,q)$ if $q \in \{ 8,32 \}$.
DOI :
10.37236/7348
Classification :
51A50, 05B25
Mots-clés : dual polar space, classical hyperplane, non-classical hyperplane
Mots-clés : dual polar space, classical hyperplane, non-classical hyperplane
@article{10_37236_7348,
author = {Bart De Bruyn},
title = {Non-classical hyperplanes of finite thick dual polar spaces},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/7348},
zbl = {1383.51004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7348/}
}
Bart De Bruyn. Non-classical hyperplanes of finite thick dual polar spaces. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7348
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