On subspace arrangements of type D

Let D n;k denote the subspace arrangement formed by all linear subspaces in R n given by equations of the form k. Some important topological properties of such a subspace arrangement depend on the topology of its intersection lattice. In previous work on a larger class of subspace arrangements by Bjj orner & Sagan BS] the topology of the intersection lattice L(D n;k) = n;k turned out to be a particularly interesting and diicult case. We prove in this paper that Pure((