Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes

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The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [Ka]. This theorem implies the conjecture of R. Stanley on the unimodularity of the generalized $h$-vector. In this paper we strengthen Karu's theorem by introducing a canonical bilinear form $(\cdot ,\cdot)_Φ$ on the intersection cohomology $IH(Φ)$ of a complete fan $Φ$ and proving the Hodge-Riemann bilinear relations for $(\cdot ,\cdot)_Φ$.
Final version to appear in Indiana University Mathematics Journal

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Algebraic Geometry, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/66576

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0302236
 http://arxiv.org/abs/math/0302236

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arXiv