Hard Lefschetz Theorem for Nonrational Polytopes

Details Hard Lefschetz Theorem for Nonrational Polytopes Hard Lefschetz Theorem for Nonrational Polytopes

2001-12-09

arxiv.org/abs/math/0112087v4

Mathematics

Algebraic Geometry

25 pages, a few errors corrected

Scientific paper

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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