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

P. Bressler; V. A. Lunts

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arXiv · math/0302236

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

P. Bressler·V. A. Lunts

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Abstract

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 $(\cdot ,\cdot)_Φ$.

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BibTeX RIS

P. Bressler, V. A. Lunts. 2003-09-17. Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes. https://arxiv.org/abs/math/0302236

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