ISSN:
1420-8946
Keywords:
Keywords. Intersection homology, toric varieties, polytopes, g-polynomial.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000140050098
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