Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes Paul BresslerValery Lunts 14M52B55Nalgebraic geometryconvex geometrytoric varietiesintersection cohomology The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [8]. 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 $(\cdot,\cdot)_{\Phi}$ on the intersection cohomology $IH(\Phi)$ of a complete fan $\Phi$ and proving the Hodge-Riemann bilinear relations for $(\cdot,\cdot)_{\Phi}$. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2528 10.1512/iumj.2005.54.2528 en Indiana Univ. Math. J. 54 (2005) 263 - 308 state-of-the-art mathematics http://iumj.org/access/