Hard Lefschetz theorem for simple polytopes
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 2, pp. 227-239.

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Summary: 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.
Keywords: simple polytopes, simplicial fans, hard Lefschetz theorem, Hodge-Riemann-Minkowski bilinear relations
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     author = {Fleming, Balin and Karu, Kalle},
     title = {Hard {Lefschetz} theorem for simple polytopes},
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Fleming, Balin; Karu, Kalle. Hard Lefschetz theorem for simple polytopes. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 2, pp. 227-239. http://geodesic.mathdoc.fr/item/JAC_2010__32_2_a3/