Arrangements in Unitary and Orthogonal Geometry over Finite Fields

@article{Graham1985ArrangementsIU,
  title={Arrangements in Unitary and Orthogonal Geometry over Finite Fields},
  author={Ronald L. Graham and Louis Solomon},
  journal={J. Comb. Theory, Ser. A},
  year={1985},
  volume={38},
  pages={217-229}
}
Let V be an n-dimensional vector space over F,. Let @ be a Hermitian form with respect to an automorphism u with u2 = 1. If u = 1 assume that q is odd. Let I be the arrangement of hyperplanes of V which are non-isotropic with respect to Cp, and let L be the intersection lattice of d. We prove that the characteristic polynomial of L has n v roots 1, q,.... qnmv-’ where v is the Witt index of @. (