Hard Lefschetz theorem for nonrational polytopes
نویسندگان
چکیده
منابع مشابه
Hard Lefschetz Theorem for Nonrational Polytopes
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 gener...
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McMullen’s proof of the Hard Lefschetz Theorem for simple polytopes is studied, and a new proof of this theorem that uses conewise polynomial functions on a simplicial fan is provided.
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Proofs of these relations may be found in [1, 2, 3]. If the polytope ∆ is not simple, then the relations above are not true. A polytope ∆ is said to be integral provided all its vertices belong to the integer lattice. With each integral convex polytope ∆ one associates the toric variety X = X(∆) (see [4, 5, 6, 7]). This is a projective complex algebraic variety, singular in general. It turns ou...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2004
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-004-0358-3