Inventiones mathematicae

, Volume 157, Issue 2, pp 419-447

First online:

Hard Lefschetz theorem for nonrational polytopes

  • Kalle KaruAffiliated withMathematics Department, University of British Columbia Email author 

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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.