Intersection cohomology of quotients of nonsingular varieties

2001/01/31 by Young-Hoon Kiem
Mathematics · #math.AG #math.SG

paper · pdf

published as Inventiones Mathematicae 155, 2004

arxiv created 2004/02/27 · arxiv updated 2009/11/30

Abstract

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.

Related

• Intersection cohomology without spaces
• The Decomposition Theorem and the Intersection Cohomology of Quotients in Algebraic Geometry
• From moment graphs to intersection cohomology
• Intersection cohomology on nonrational polytopes
• Refined intersection homology on non-Witt spaces