Commentarii Mathematici Helvetici

, Volume 74, Issue 3, pp 442–455 | Cite as

Intersection homology of toric varieties and a conjecture of Kalai

  • T. Braden
  • R. MacPherson


We prove an inequality, conjectured by Kalai, relating the g-polynomials of a polytope P, a face F, and the quotient polytope P/F, in the case where P is rational. We introduce a new family of polynomials g(P,F), which measures the complexity of the part of P“far away” from the face F; Kalai's conjecture follows from the nonnegativity of these polynomials. This nonnegativity comes from showing that the restriction of the intersection cohomology sheaf on a toric variety to the closure of an orbit is a direct sum of intersection homology sheaves.

Keywords. Intersection homology, toric varieties, polytopes, g-polynomial. 


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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • T. Braden
    • 1
  • R. MacPherson
    • 2
  1. 1.Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA, e-mail: braden@math.harvard.eduUSA
  2. 2.Fuld Hall, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA USA

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