Hyperbolic localization of intersection cohomology

2002/02/28 by Tom Braden
Mathematics · #math.AG #msc:55N33 #msc:14L30

paper · pdf

published as Transformation Groups 8 (2003), no. 3, 209-216 · 9 pages; extensive revisions

arxiv created 2003/07/29 · arxiv updated 2009/11/30

Abstract

For a normal variety X defined over an algebraically closed field with an action of the multiplicative group G_m, we consider the ``hyperbolic localization'' functor from D^b(X) to D^b(X^T), which localizes using closed supports in the directions flowing into the fixed points, and compact supports in the directions flowing out. We show that the hyperbolic localization of the intersection cohomology sheaf is a direct sum of intersection cohomology sheaves.

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