The hyperplanes of {${DW(5,2)}$}

Abstract

A (geometric) hyperplane of a geometry is a proper subspace meeting every line. We present a complete list of the hyperplane classes of the symplectic dual polar space {\small $DW(5,2)$}. Theoretical results from Shult, Pasini and Shpectorov, and the author guarantee the existence of certain hyperplanes. To complete the list, we use a backtrack algorithm implemented in the computer algebra system GAP. We finally investigate what hyperplane classes arise from which projective embeddings of {\small $DW(5,2)$}.