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 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 DW(5, 2).

Keywords:

• Primary 05E15, 05E20, 51A50, 51E20
• Backtrack algorithm
• dual polar spaces
• hyperplanes
• subspace lattice
• symplectic polar space