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Hard Lefschetz theorem for nonrational polytopes

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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.

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  1. Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada, V6T 1Z2

    Kalle Karu

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  1. Kalle Karu
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Karu, K. Hard Lefschetz theorem for nonrational polytopes. Invent. math. 157, 419–447 (2004). https://doi.org/10.1007/s00222-004-0358-3

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  • DOI: https://doi.org/10.1007/s00222-004-0358-3

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