  The purpose of this paper is to provide a way to compute the intersection
cohomology of the GIT quotient of a nonsingular projective variety. We show
that the middle perversity intersection cohomology of the GIT quotient $M//G$
is naturally embedded into the $G$ equivariant cohomology of $M^{ss}$ under an
assumption satisfied by many interesting spaces. This embedding enables us to
compute the intersection pairing in terms of the cup product structure of the
equivariant cohomology ring. We also show that the image is a subspace defined
by truncation. Overall, we can compute the intersection cohomology as a graded
vector space with a nondegenerate pairing.
