Inventiones mathematicae

, Volume 157, Issue 2, pp 419–447

Hard Lefschetz theorem for nonrational polytopes


    • Mathematics DepartmentUniversity of British Columbia

DOI: 10.1007/s00222-004-0358-3

Cite this article as:
Karu, K. Invent. math. (2004) 157: 419. doi:10.1007/s00222-004-0358-3


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.

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© Springer-Verlag 2004