{
  "id": "math/0302236",
  "version": "v3",
  "published": "2003-02-19T17:10:46.000Z",
  "updated": "2003-09-17T16:15:41.000Z",
  "title": "Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes",
  "authors": [
    "P. Bressler",
    "V. A. Lunts"
  ],
  "comment": "Final version to appear in Indiana University Mathematics Journal",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "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 $(\\cdot ,\\cdot)_{\\Phi}$ on the intersection cohomology $IH(\\Phi)$ of a complete fan $\\Phi$ and proving the Hodge-Riemann bilinear relations for $(\\cdot ,\\cdot)_{\\Phi}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-09-17T16:15:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hard lefschetz theorem",
      "intersection cohomology",
      "nonrational polytopes",
      "hodge-riemann relations",
      "hodge-riemann bilinear relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2236B"
    }
  }
}