Lower Bounds for the Generalized h-Vectors of Centrally Symmetric Polytopes

Details Lower Bounds for the Generalized h-Vectors of Centrally Symmetric Polytopes Lower Bounds for the Generalized h-Vectors of Centrally Symmetric Polytopes

2003-01-26

arxiv.org/abs/math/0301303v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

In a previous article, we proved tight lower bounds for the coefficients of the generalized $h$-vector of a centrally symmetric rational polytope using intersection cohomology of the associated projective toric variety. Here we present a new proof based on the theory of combinatorial intersection cohomology developed by Barthel, Brasselet, Fieseler and Kaup. This theory is also valid for nonrational polytopes when there are no corresponding toric varieties. So we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational.

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