  Schubert varieties of hyperplane arrangements, also known as matroid Schubert
varieties, play an essential role in the proof of the Dowling-Wilson conjecture
and in Kazhdan-Lusztig theory for matroids. We study these varieties as
equivariant compactifications of affine spaces, and give necessary and
sufficient conditions to characterize them. We also generalize the theory to
include partial compactifications and morphisms between them. Our results
resemble the correspondence between toric varieties and polyhedral fans.
