Non-Classical Hyperplanes of Finite Thick Dual Polar Spaces

Bart De Bruyn

Abstract


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 $q \in \{ 8,32 \}$.

Keywords


Dual polar space, Classical Hyperplane, Non-classical Hyperplane

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