Geometric construction of linear complex of planes of B 3 type

Abstract

Using invariant geometric images of a trivector of the type (884; 400), we construct its basic group of automorphisms. We formulate and prove a theorem on necessary and sufficient conditions for determining all planes of a linear complex associated with a trivector of the given type up to linear transformations of its automorphism group. Proving the theorem, we find all kinds of singular lines and construct the polar hyperplanes for nonsingular lines