Non-classical hyperplanes of finite thick dual polar spaces (Q1700807)

Summary: 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 \(q \in \{8,32\}\).