Intersection cohomology of quotients of nonsingular varieties

Details Intersection cohomology of quotients of nonsingular varieties Intersection cohomology of quotients of nonsingular varieties

2001-01-30

arxiv.org/abs/math/0101254v3

Inventiones Mathematicae 155, 2004

Mathematics

Algebraic Geometry

Scientific paper

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.

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