We show that the center of a flat graded deformation of a standard Koszul
algebra behaves in many ways like the torus-equivariant cohomology ring of an
algebraic variety with finite fixed-point set. In particular, the center acts
by characters on the deformed standard modules, providing a "localization map."
We construct a universal graded deformation, and show that the spectrum of its
center is supported on a certain arrangement of hyperplanes which is orthogonal
to the arrangement coming the Koszul dual algebra. This is an algebraic version
of a duality discovered by Goresky and MacPherson between the equivariant
cohomology rings of partial flag varieties and Springer fibers; we recover and
generalize their result by showing that the center of the universal deformation
for the ring governing a block of parabolic category O for
gln​ is isomorphic to the equivariant cohomology of a Spaltenstein
variety. We also identify the center of the deformed version of the "category
O" of a hyperplane arrangement (defined by the authors in a
previous paper) with the equivariant cohomology of a hypertoric variety.Comment: 39 pages; v3: final versio