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

2005; Indiana University; Volume: 54; Issue: 1 Linguagem: Inglês

10.1512/iumj.2005.54.2528

1943-5266

Paul Bressler, Valery A. Lunts,

Geometric and Algebraic Topology

The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [9]. 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 (.,.) Φ on the intersection cohomology IH(Φ) of a complete fan Φ and proving the Hodge-Riemann bilinear relations for (.,.) Φ .