Intersection cohomology of $S^1$ symplectic quotients and small   resolutions
  We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the $S^1$ equivariant cohomology of the original symplectic manifold and the fixed point data. The key idea is the construction of a small resolution of the symplectic quotient. 
Eugene Lerman and Susan Tolman