EQUIVARIANT INTERSECTION COHOMOLOGY OF SEMI-STABLE POINTS

The main result of the paper is that the equivariant intersection coho mology of the semistable points on a complex projective variety, for t he action of a complex reductive group, may be determined from the equ ivariant intersection cohomology of the semi-stable points for the act ion of a maximal torus. It extends the work of Brion who considered th e smooth case using equivariant cohomology. Equivariant intersection c ohomology is a theory due to Brylinski and the second author. As an ap plication, a surprising relation between the intersection cohomology o f Chow hypersurfaces is established in the last section of the paper.