Kalle Karu
Published 2001-12-09, updated 2002-12-17Version 4
The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a general polytope.
Comments: 25 pages, a few errors corrected
Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes
On polytopes simple in edges
The decomposition theorem and the Intersection cohomology of the Satake-Baily-Borel compactification of ${\mathcal A}_g$ for small genus
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